Graph classes with structured neighborhoods and algorithmic applications
Given a graph in any of the following graph classes: trapezoid graphs, circular permutation graphs, convex graphs, Dilworth k graphs, k-polygon graphs, circular arc graphs and complements of k-degenerate graphs, we show how to compute decompositions with the number of d-neighborhoods bounded by a po...
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| Published in: | Theoretical computer science Vol. 511; pp. 54 - 65 |
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| Language: | English |
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04.11.2013
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| ISSN: | 0304-3975, 1879-2294 |
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| Abstract | Given a graph in any of the following graph classes: trapezoid graphs, circular permutation graphs, convex graphs, Dilworth k graphs, k-polygon graphs, circular arc graphs and complements of k-degenerate graphs, we show how to compute decompositions with the number of d-neighborhoods bounded by a polynomial of the input size. Combined with results of Bui-Xuan, Telle and Vatshelle (2013) [1] this leads to polynomial time algorithms for a large class of locally checkable vertex subset and vertex partitioning problems on all of these graph classes. The boolean-width of a graph is related to the number of 1-neighborhoods and our results imply that any of these graph classes have boolean-width O(logn). |
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| AbstractList | Given a graph in any of the following graph classes: trapezoid graphs, circular permutation graphs, convex graphs, Dilworth k graphs, k-polygon graphs, circular arc graphs and complements of k-degenerate graphs, we show how to compute decompositions with the number of d-neighborhoods bounded by a polynomial of the input size. Combined with results of Bui-Xuan, Telle and Vatshelle (2013) [1] this leads to polynomial time algorithms for a large class of locally checkable vertex subset and vertex partitioning problems on all of these graph classes. The boolean-width of a graph is related to the number of 1-neighborhoods and our results imply that any of these graph classes have boolean-width O(logn). |
| Author | Belmonte, Rémy Vatshelle, Martin |
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| Keywords | Graph decomposition Boolean-width Graph classes Vertex partitioning problems |
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