Rainbow vertex pair-pancyclicity of strongly edge-colored graphs

Abstract

An edge-colored graph is rainbow if no two edges of the graph have the same color. A strongly edge-colored graph is an edge-colored graph such that every path of length 3 is rainbow. We call an edge-colored graph G c is rainbow vertex pairpancyclic if any two vertices in G c are contained in a rainbow cycle of length l for each l with 3 ≤ l ≤ n. In this paper, we show that every strongly edge-colored graph G c of order n with minimum degree δ ≥ 2n 3 + 1 is rainbow vertex pair-pancyclicity.