Chetwynd, Amanda G. and Hilton, A. J. W. (1990) The chromatic index of graphs with large maximum degree, where the number of vertices of maximum degree is relatively small. Journal of Combinatorial Theory, Series B, 48 (1). ISSN 0095-8956Full text not available from this repository.
By Vizing's theorem, the chromatic index χ′(G) of a simple graph G satisfies Δ(G) ≤ χ′(G) ≤ Δ(G) + 1; if χ′(G) = Δ(G), then G is Class 1, and if χ′(G) = Δ(G) + 1, then G is Class 2. We describe the structure of Class 2 graphs satisfying the inequality , where r is the number of vertices of maximum degree. A graph G is critical if G is Class 2 and χ′(H) < χ′(G) for all proper subgraphs H of G. We also describe the structure of critical graphs satisfying the inequality above. We also deduce, as a corollary, an earlier result of ours that a regular graph G of even order satisfying is Class 1.
|Journal or Publication Title:||Journal of Combinatorial Theory, Series B|
|Subjects:||Q Science > QA Mathematics|
|Departments:||Faculty of Science and Technology > Mathematics and Statistics|
|Deposited By:||Prof Amanda Chetwynd|
|Deposited On:||25 Nov 2008 08:50|
|Last Modified:||01 Jan 2017 01:28|
Actions (login required)