Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4651153 | Discrete Mathematics | 2007 | 5 Pages |
Abstract
A hypergraph H is linear if no two distinct edges of H intersect in more than one vertex and loopless if no edge has size one. A q-edge-colouring of H is a colouring of the edges of H with q colours such that intersecting edges receive different colours. We use ÎH to denote the maximum degree of H. A well-known conjecture of ErdÅs, Farber and Lovász is equivalent to the statement that every loopless linear hypergraph on n vertices can be n-edge-coloured. In this paper we show that the conjecture is true when the partial hypergraph S of H determined by the edges of size at least three can be ÎS-edge-coloured and satisfies ÎS⩽3. In particular, the conjecture holds when S is unimodular and ÎS⩽3.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Bill Jackson, G. Sethuraman, Carol Whitehead,