V.G. Vizing proved that the edge-chromatic number x1 of any multigraph M with maximum degree Δ(M) and maximum multiplicity μ(M) is Δ(M)+μ(M). 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 proofs we replace arguments about 'fan sequences' with counting arguments.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics