Skip to Main content Skip to Navigation
Journal articles

Clique-transversal sets and weak 2-colorings in graphs of small maximum degree

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.
Document type :
Journal articles
Complete list of metadata

Cited literature [22 references]  Display  Hide  Download

https://hal.inria.fr/hal-00988213
Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>
Submitted on : Wednesday, May 7, 2014 - 4:23:29 PM
Last modification on : Wednesday, December 11, 2019 - 5:10:02 PM
Long-term archiving on: : Thursday, August 7, 2014 - 11:40:32 AM

File

1273-4292-1-PB.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00988213, version 1

Collections

Citation

Gábor Bacsó, Zsolt Tuza. Clique-transversal sets and weak 2-colorings in graphs of small maximum degree. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2009, 11 (2), pp.15--24. ⟨hal-00988213⟩

Share

Metrics

Record views

518

Files downloads

890