Clique-transversal sets and weak 2-colorings in graphs of small maximum degreeReport as inadecuate




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1 MTA SZTAKI - Computer and Automation Research Institute Budapest 2 Department of Computer Science and Systems Technology Veszprem

Abstract : 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.





Author: Gábor Bacsó - Zsolt Tuza -

Source: https://hal.archives-ouvertes.fr/



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