Rainbow connection numbers of line graphs

Abstract

A path in an edge-coloring graph G, where adjacent edges may be colored the same, is called a rainbow path if no two edges of G are colored the same. A nontrivial connected graph G is rainbow connected if for any two vertices of G there is a rainbow path connecting them. The rainbow connection number of G, denoted rc(G), is defined as the minimum number of colors by using which there is coloring such that G is rainbow connected. In this paper, we study the rainbow connection numbers of line graphs of triangle-free graphs, and particularly, of 2-connected triangle-free graphs according to their ear decompositions.