A new condition for a graph having conflict free connection number 2

DOI: 10.18173/2354-1059.2021-0003

Abstract

A path in an edge-coloured graph is called conflict-free if there is a colour used on exactly one of its edges. An edge-coloured graph is said to be conflict-free connected if any two distinct vertices of the graph are connected by a conflict-free path. The conflict-free connection number, denoted by cf c(G), is the smallest number of colours needed in order to make G conflict-free connected. In this paper, we give a new condition to show that a connected non-complete graph G having cf c(G) = 2. This is an extension of a result by Chang et al. [1].