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On Strict (Outer-)Confluent Graphs Henry F orster, Robert Ganian, - PowerPoint PPT Presentation

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On Strict (Outer-)Confluent Graphs Henry F orster, Robert Ganian, Fabian Klute, Martin N ollenburg Graph Drawing 2019 September 18, 2019 1/21 Confluence Technique to bundle edges 2/21 Henry F orster, Robert Ganian, Fabian Klute,

  1. Our Results subtree-filament string outer-string interval-filament co-comparability strict-confluent unit interval polygon-circle series-parallel strict-outerconfluent pseudo-split chordal circle-trapezoid circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  2. Our Results subtree-filament string outer-string interval-filament co-comparability strict-confluent unit interval polygon-circle series-parallel strict-outerconfluent pseudo-split chordal circle-trapezoid circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  3. Our Results subtree-filament string outer-string interval-filament co-comparability strict-confluent unit interval polygon-circle series-parallel strict-outerconfluent pseudo-split chordal circle-trapezoid ∆ -confluent circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  4. Our Results subtree-filament string outer-string interval-filament co-comparability strict-confluent unit interval polygon-circle series-parallel strict-outerconfluent pseudo-split chordal circle-trapezoid distance-hereditary ∆ -confluent circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  5. Our Results subtree-filament string outer-string interval-filament co-comparability strict-confluent unit interval polygon-circle series-parallel strict-outerconfluent pseudo-split chordal tree-like ∆ -strict-outerconfluent circle-trapezoid distance-hereditary ∆ -confluent circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  6. Our Results subtree-filament string outer-string interval-filament co-comparability strict-confluent unit interval polygon-circle series-parallel strict-outerconfluent pseudo-split chordal tree-like ∆ -strict-outerconfluent circle-trapezoid distance-hereditary ∆ -confluent circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  7. Our Results subtree-filament string outer-string interval-filament co-comparability strict-confluent unit interval polygon-circle series-parallel strict-outerconfluent pseudo-split chordal tree-like ∆ -strict-outerconfluent circle-trapezoid distance-hereditary ∆ -confluent circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  8. Our Results subtree-filament string outer-string interval-filament co-comparability strict-confluent unit interval polygon-circle bounded series-parallel cliquewidth strict-outerconfluent pseudo-split chordal tree-like ∆ -strict-outerconfluent circle-trapezoid distance-hereditary ∆ -confluent circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  9. Our Results subtree-filament string outer-string interval-filament co-comparability strict-confluent unit interval polygon-circle bounded series-parallel cliquewidth strict-outerconfluent pseudo-split chordal tree-like ∆ -strict-outerconfluent circle-trapezoid distance-hereditary ∆ -confluent circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  10. Our Results subtree-filament string outer-string interval-filament co-comparability strict-confluent unit interval polygon-circle bounded series-parallel cliquewidth strict-outerconfluent pseudo-split chordal tree-like ∆ -strict-outerconfluent ? circle-trapezoid distance-hereditary ∆ -confluent circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  11. Our Results Cop number: c [Gavenˇ ciak et al. 18] subtree-filament string outer-string interval-filament co-comparability strict-confluent unit interval polygon-circle bounded series-parallel cliquewidth strict-outerconfluent pseudo-split chordal tree-like ∆ -strict-outerconfluent ? circle-trapezoid distance-hereditary ∆ -confluent circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  12. Our Results Cop number: c [Gavenˇ ciak et al. 18] subtree-filament 3 ≤ c ≤ 15 string outer-string interval-filament co-comparability strict-confluent unit interval polygon-circle bounded series-parallel cliquewidth strict-outerconfluent pseudo-split chordal tree-like ∆ -strict-outerconfluent ? circle-trapezoid distance-hereditary ∆ -confluent circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  13. Our Results Cop number: c [Gavenˇ ciak et al. 18] subtree-filament 3 ≤ c ≤ 15 3 ≤ c ≤ 4 string outer-string interval-filament co-comparability strict-confluent unit interval polygon-circle bounded series-parallel cliquewidth strict-outerconfluent pseudo-split chordal tree-like ∆ -strict-outerconfluent ? circle-trapezoid distance-hereditary ∆ -confluent circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  14. Our Results Cop number: c [Gavenˇ ciak et al. 18] subtree-filament 3 ≤ c ≤ 15 3 ≤ c ≤ 4 c = 2 string outer-string interval-filament co-comparability strict-confluent unit interval polygon-circle bounded series-parallel cliquewidth strict-outerconfluent pseudo-split chordal tree-like ∆ -strict-outerconfluent ? circle-trapezoid distance-hereditary ∆ -confluent circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  15. Our Results Cop number: c [Gavenˇ ciak et al. 18] subtree-filament 3 ≤ c ≤ 15 3 ≤ c ≤ 4 c = 2 string outer-string interval-filament co-comparability c = 1 strict-confluent unit interval polygon-circle bounded series-parallel cliquewidth strict-outerconfluent pseudo-split chordal tree-like ∆ -strict-outerconfluent ? c = 1 circle-trapezoid distance-hereditary ∆ -confluent circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  16. Our Results Cop number: c [Gavenˇ ciak et al. 18] subtree-filament 3 ≤ c ≤ 15 3 ≤ c ≤ 4 c = 2 string outer-string interval-filament co-comparability c = 1 strict-confluent unit interval polygon-circle bounded c = 2 series-parallel cliquewidth strict-outerconfluent pseudo-split chordal tree-like ∆ -strict-outerconfluent ? c = 1 circle-trapezoid distance-hereditary ∆ -confluent circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  17. Our Results Cop number: c [Gavenˇ ciak et al. 18] subtree-filament 3 ≤ c ≤ 15 3 ≤ c ≤ 4 c = 2 string outer-string interval-filament ? co-comparability c = 1 strict-confluent unit interval polygon-circle bounded c = 2 series-parallel cliquewidth strict-outerconfluent pseudo-split chordal tree-like ∆ -strict-outerconfluent ? c = 1 circle-trapezoid distance-hereditary ∆ -confluent circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  18. Our Results Cop number: c [Gavenˇ ciak et al. 18] subtree-filament 3 ≤ c ≤ 15 3 ≤ c ≤ 4 c = 2 string outer-string interval-filament ? co-comparability c = 1 strict-confluent unit interval polygon-circle bounded c = 2 series-parallel cliquewidth strict-outerconfluent pseudo-split chordal tree-like ∆ -strict-outerconfluent ? c = 1 circle-trapezoid distance-hereditary ∆ -confluent circular arc strict bipartite outerconfluent circle bipartite permutation bipartite permutation trapezoid comparability bipartite permutation ∩ domino-free 6/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  19. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  20. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A path 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  21. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A path 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  22. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A path 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  23. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A path 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  24. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A path 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  25. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A path 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  26. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A path 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  27. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A path 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  28. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A path 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  29. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A path 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  30. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A path 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  31. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  32. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  33. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  34. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  35. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  36. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  37. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  38. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  39. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  40. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  41. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  42. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  43. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  44. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  45. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  46. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  47. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  48. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  49. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  50. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  51. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  52. Cops and Robbers Simple two player game on a graph Cop player has k cop tokens Robber player has 1 robber token In a turn player can move their token to adjacent vertices Robber is caught if it coincides with a cop Cop-number: What is the smallest k such that cop player wins? Example: A circle 7/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  53. Cops and Robbers meeting SOC Graphs Result: Strict outer-confluent graphs have cop-number 2 8/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  54. Cops and Robbers meeting SOC Graphs Result: Strict outer-confluent graphs have cop-number 2 u v r Using one cop, robber is “locked” between u and v 8/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  55. Cops and Robbers meeting SOC Graphs Result: Strict outer-confluent graphs have cop-number 2 u v r Using one cop, robber is “locked” between u and v 8/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  56. Cops and Robbers meeting SOC Graphs Result: Strict outer-confluent graphs have cop-number 2 u v r Using one cop, robber is “locked” between u and v 8/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  57. Cops and Robbers meeting SOC Graphs Result: Strict outer-confluent graphs have cop-number 2 u v r Using one cop, robber is “locked” between u and v 8/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  58. Cops and Robbers meeting SOC Graphs Result: Strict outer-confluent graphs have cop-number 2 u v r Using one cop, robber is “locked” between u and v 8/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  59. Cops and Robbers meeting SOC Graphs Result: Strict outer-confluent graphs have cop-number 2 u v r Using one cop, robber is “locked” between u and v 8/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  60. Cops and Robbers meeting SOC Graphs Result: Strict outer-confluent graphs have cop-number 2 u v r Using one cop, robber is “locked” between u and v 8/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  61. Cops and Robbers meeting SOC Graphs Result: Strict outer-confluent graphs have cop-number 2 u v r Using one cop, robber is “locked” between u and v 8/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  62. Cops and Robbers meeting SOC Graphs Result: Strict outer-confluent graphs have cop-number 2 u v r Using one cop, robber is “locked” between u and v 8/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  63. Cops and Robbers meeting SOC Graphs Result: Strict outer-confluent graphs have cop-number 2 u v r Using one cop, robber is “locked” between u and v 8/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  64. Cops and Robbers meeting SOC Graphs Result: Strict outer-confluent graphs have cop-number 2 u v r Using one cop, robber is “locked” between u and v 8/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

  65. Cops and Robbers meeting SOC Graphs Result: Strict outer-confluent graphs have cop-number 2 u v r Using one cop, robber is “locked” between u and v How to lock robber to smaller set of vertices? 8/21 Henry F¨ orster, Robert Ganian, Fabian Klute, Martin N¨ ollenburg · On SOC Graphs

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