Proper path-factors and interval edge-coloring of (3,4)-biregular bigraphs
Combinatorics
2007-05-23 v1
Abstract
An interval coloring of a graph G is a proper coloring of E(G) by positive integers such that the colors on the edges incident to any vertex are consecutive. A (3,4)-biregular bigraph is a bipartite graph in which each vertex of one part has degree 3 and each vertex of the other has degree 4; it is unknown whether these all have interval colorings. We prove that G has an interval coloring using 6 colors when G is a (3,4)-biregular bigraph having a spanning subgraph whose components are paths with endpoints at 3-valent vertices and lengths in {2,4,6,8}. We provide sufficient conditions for the existence of such a subgraph.
Keywords
Cite
@article{arxiv.0704.2650,
title = {Proper path-factors and interval edge-coloring of (3,4)-biregular bigraphs},
author = {Armen S. Asratian and Carl Johan Casselgren and Jennifer Vandenbussche and Douglas B. West},
journal= {arXiv preprint arXiv:0704.2650},
year = {2007}
}
Comments
11 pages, 2 figures