On the Equitable Edge-Coloring of 1-Planar Graphs and Planar Graphs

摘要

An edge-coloring of a graph G is equitable if, for each vertex v of G, the number of edges of any one color incident with v differs from the number of edges of any other color incident with v by at most one. In the paper, we prove that every 1-planar graph has an equitable edge-coloring with k colors for any integer , and every planar graph has an equitable edge-coloring with k colors for any integer k >= 12 .