Clique-transversal sets and weak 2-colorings in graphs of small maximum degree
Author:
Bacsó Gábor,Tuza Zsolt
Abstract
Graphs and Algorithms
International audience
A clique-transversal set in a graph is a subset of the vertices that meets all maximal complete subgraphs on at least two vertices. We prove that every connected graph of order n and maximum degree three has a clique-transversal set of size left perpendicular19n/30 + 2/15right perpendicular. This bound is tight, since 19n/30 - 1/15 is a lower bound for infinitely many values of n. We also prove that the vertex set of any connected claw-free graph of maximum degree at most four, other than an odd cycle longer than three, can be partitioned into two clique-transversal sets. The proofs of both results yield polynomial-time algorithms that find corresponding solutions.
Publisher
Centre pour la Communication Scientifique Directe (CCSD)
Subject
Discrete Mathematics and Combinatorics,General Computer Science,Theoretical Computer Science
Cited by
1 articles.
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