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...

Full description

Saved in:
Bibliographic Details
Published in:Theoretical computer science Vol. 511; pp. 54 - 65
Main Authors: Belmonte, Rémy, Vatshelle, Martin
Format: Journal Article
Language:English
Published: Elsevier B.V 04.11.2013
Subjects:
Boolean-width
Graph classes
Graph decomposition
Vertex partitioning problems
Graph decomposition
Boolean-width
Graph classes
Vertex partitioning problems
ISSN:0304-3975, 1879-2294
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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).
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2013.01.011