Rainbow vertex pair-pancyclicity of strongly edge-colored graphs.

An edge-colored graph is rainbow if no two edges of the graph have the same color. An edge-colored graph Gc is called properly colored if every two adjacent edges of Gc receive distinct colors in Gc. A strongly edge-colored graph is a proper edge-colored graph such that every path of length 3 is rainbow. We call an edge-colored graph Gc rainbow vertex pair-pancyclic if any two vertices in Gc 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 Gc of order n with minimum degree δ ≤ 2n/3 + 1 is rainbow vertex pair-pancyclicity. [ABSTRACT FROM AUTHOR]