Elsevier

Discrete Mathematics

Volume 311, Issue 12, 28 June 2011, Pages 996-1005
Discrete Mathematics

Ohba’s conjecture for graphs with independence number five

https://doi.org/10.1016/j.disc.2011.02.026Get rights and content
Under an Elsevier user license
open archive

Abstract

Ohba has conjectured that if G is a k-chromatic graph with at most 2k+1 vertices, then the list chromatic number or choosability ch(G) of G is equal to its chromatic number χ(G), which is k. It is known that this holds if G has independence number at most three. It is proved here that it holds if G has independence number at most five. In particular, and equivalently, it holds if G is a complete k-partite graph and each part has at most five vertices.

Keywords

Chromatic number
Vertex coloring
List coloring
List chromatic number
Choosability
Complete multipartite graph

Cited by (0)