L-Factors and Adjacent Vertex-Distinguishing Edge-Weighting
Yinghua Duan 1, Hongliang Lu 2*, Qinglin Yu 31 Department of Mathematics, Beijing National Day School, Beijing, PR China.
2 School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, PR China.
2 Department of Mathematics and Statistics, Thompson Rivers University, Kamloops, BC, Canada.
Received 8 April 2011; Accepted (in revised version) 29 December 2011
Available online 27 April 2012
An edge-weighting problem of a graph $G$ is an assignment of an integer weight to each edge $e$. Based on an edge-weighting problem, several types of vertex-coloring problems are put forward. A simple observation illuminates that the edge-weighting problem has a close relationship with special factors of the graphs. In this paper, we generalise several earlier results on the existence of factors with pre-specified degrees and hence investigate the edge-weighting problem --- and in particular, we prove that every $4$-colorable graph admits a vertex-coloring $4$-edge-weighting.AMS subject classifications: 05C70, 05C15
Key words: Edge-weighting, vertex-coloring, L-factor.
Email: email@example.com (H. Lu), firstname.lastname@example.org (Y. Duan), email@example.com (Q. Yu)