Color Degree and Heterochromatic Paths in Edge-Colored Graphs

Abstract

Let \(G\) be an edge-colored graphs. A heterochromatic path of \(G\) is such a path in which no two edges have the same color. Let \(g^c(G)\) and \(d^c(v)\) denote the heterochromatic girth and the color degree of a vertex \(v\) of \(G\), respectively. In this paper, some color degree and heterochromatic girth conditions for the existence of heterochromatic paths are obtained.