Elsevier

Discrete Mathematics

Volume 313, Issue 19, 6 October 2013, Pages 1856-1860
Discrete Mathematics

Achromatic number of collections of paths and cycles

https://doi.org/10.1016/j.disc.2012.08.008Get rights and content
Under an Elsevier user license
open archive

Abstract

A complete colouring of a simple graph G is a proper vertex colouring such that each pair of colours appears together on at least one edge. The achromatic number ψ(G) is the greatest number of colours in such a colouring.

We give simple necessary and sufficient conditions for a graph of maximum degree 2 to have a complete colouring with k colours, provided the graph is large enough, and use this to give the achromatic number for such a graph.

Keywords

Achromatic number
Cycles
Paths

Cited by (0)