## V.G. Wing proved that the edge-chromatic 11umber x' of any multigraph M with m&mum degree A(M) aud maximum multiplicity p(M) is A(M)+pLM). In this paper we present a new method for proving this and other related results that are due to Gol'dberg, Anderson, Ore, Shannon, and Vizing. In our proof
A new method for proving chromatic uniqueness of graphs
โ Scribed by Ru-Ying Liu; Lian-Chang Zhao
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 359 KB
- Volume
- 171
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
We give a brief survey on a new method for proving the chromatic uniqueness of graphs by their adjoint polynomials. We obtain some simpler proofs of relevant theorems and a new family of chromatically unique graphs.
๐ SIMILAR VOLUMES
Du, Q., On o-polynomials and a class of chromatically unique graphs, Discrete Mathematics 115 (1993) 153-165. Let cr(G)=C:,,aicr '-' be the u-polynomial of a graph G. We ask the question: When k and a, are given, what is the largest possible value of ai(O < i < k) for any graph G? In this paper, thi
## Abstract In this article we first give an upper bound for the chromatic number of a graph in terms of its degrees. This bound generalizes and modifies the bound given in 11. Next, we obtain an upper bound of the order of magnitude ${\cal O}({n}^{{1}-\epsilon})$ for the coloring number of a graph