Elsevier

Discrete Applied Mathematics

Volume 209, 20 August 2016, Pages 247-250
Discrete Applied Mathematics

Sufficient conditions for 2-rainbow connected graphs

https://doi.org/10.1016/j.dam.2015.10.025Get rights and content
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Abstract

An edge-coloured connected graph G is rainbow connected if each two vertices are connected by a path whose edges have distinct colours. If such a colouring uses k colours then G is called k-rainbow connected. The rainbow connection number of G, denoted by rc(G), is the minimum k such that G is k-rainbow connected. Even the problem to decide whether rc(G)=2 is NP-complete. It has been shown that if G is a connected graph of order n and size m with n22+2mn12, then 2rc(G)3.

In this paper we will present sufficient conditions for graphs G of this size to fulfil rc(G)=2 depending on vertex degrees.

Keywords

Rainbow colouring
Rainbow connected

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