2010/07/08 by Yinghua Duan, Hongliang Lu, Duan, Yinghua +3
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1007.1295
arxiv created 2010/07/08 · arxiv updated 2010/07/09
An edge weighting problem of a graph G is an assignment of an integer weight to each edge e. Based on edge weighting problem, several types of vertex-coloring problems are put forward. A simple observation illuminates that edge weighting problem has a close relationship with special factors of graphs. In this paper, we obtain several results on the existence of factors with the pre-specified degrees, which generalizes earlier results in [2, 3]. Using these results, we investigate edge-weighting problem. In particular, we prove that every 4-colorable graph admits a vertex-coloring 4-edge-weighting.