Graph classes with structured neighborhoods and algorithmic applications

Authors:
Rémy Belmonte;Martin Vatshelle
Affiliations:
-;-
Venue:
Theoretical Computer Science
Year:
2013

Citing 22
Cited 1

Decomposition of perfect graphs

Journal of Combinatorial Theory Series B
Domination in convex and chordal bipartite graphs

Information Processing Letters
Graph minors: X. obstructions to tree-decomposition

Journal of Combinatorial Theory Series B
Linear time algorithms on circular-arc graphs

Information Processing Letters
The complexity of domination problems in circle graphs

Discrete Applied Mathematics
Independence and domination in polygon graphs

Discrete Applied Mathematics
On the 2-chain subgraph cover and related problems

Journal of Algorithms
Dominations in trapezoid graphs

Information Processing Letters
Measuring the vulnerability for classes of intersection graphs

Discrete Applied Mathematics
Weighted domination of cocomparability graphs

Discrete Applied Mathematics
Polygon graph recognition

Journal of Algorithms
Efficient Algorithms for the Domination Problems on Interval and Circular-Arc Graphs

SIAM Journal on Computing
An $O(N + M)$-Time Algorithm for Finding a Minimum-WeightDominating Set in a Permutation Graph

SIAM Journal on Computing
Branch-width and well-quasi-ordering in matroids and graphs

Journal of Combinatorial Theory Series B
Algorithms for Vertex Partitioning Problems on Partial k-Trees

SIAM Journal on Discrete Mathematics
Generalized domination in chordal graphs

Nordic Journal of Computing
Certifying algorithms for recognizing interval graphs and permutation graphs

SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
On the restriction of some NP-complete graph problems to permutation graphs

FCT '85 Fundamentals of Computation Theory
Approximating clique-width and branch-width

Journal of Combinatorial Theory Series B
Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms

Journal of Computer and System Sciences
Computing role assignments of chordal graphs

Theoretical Computer Science
Fast dynamic programming for locally checkable vertex subset and vertex partitioning problems

Theoretical Computer Science

Fast dynamic programming for locally checkable vertex subset and vertex partitioning problems

Theoretical Computer Science

Quantified Score

Hi-index	5.23

Visualization

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).