Graphs with rainbow connection number two

Arnfried Kemnitz; Ingo Schiermeyer

ArticleOriginal scientific text

Title

Graphs with rainbow connection number two

Authors ¹, ²

Affiliations

Computational Mathematics, Technische Universität Braunschweig, 38023 Braunschweig, Germany
Institut für Diskrete Mathematik und Algebra, Technische Universität Bergakademie Freiberg, 09596 Freiberg, Germany

Abstract

An edge-coloured graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colours. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colours that are needed in order to make G rainbow connected. In this paper we prove that rc(G) = 2 for every connected graph G of order n and size m, where

b \in o m {n - 1} {2} + 1 \leq m \leq b \in o m {n} {2} - 1

. We also characterize graphs with rainbow connection number two and large clique number.

Keywords

ENG

edge colouring, rainbow colouring, rainbow connection

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Title

Graphs with rainbow connection number two

Affiliations

Abstract

Keywords

Bibliography