L-factors and adjacent vertex-distinguishing edge-weighting
Combinatorics
2010-07-09 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1007.1295,
title = {L-factors and adjacent vertex-distinguishing edge-weighting},
author = {Yinghua Duan and Hongliang Lu and Qinglin yu},
journal= {arXiv preprint arXiv:1007.1295},
year = {2010}
}