On Vizing's bound for the chromatic index of a multigraph

@article{Scheide2009OnVB,
  title={On Vizing's bound for the chromatic index of a multigraph},
  author={Diego Scheide and Michael Stiebitz},
  journal={Discrete Mathematics},
  year={2009},
  volume={309},
  pages={4920-4925}
}
Two of the basic results on edge coloring are Vizing’s Theorem [V.G. Vizing, On an estimate of the chromatic class of a p-graph, Diskret. Analiz. 3 (1964) 25–30 (in Russian); V.G. Vizing, The chromatic class of a multigraph, Kibernetika (Kiev) 3 (1965) 29–39 (in Russian). English translation in Cybernetics 1 32–41], which states that the chromatic index χ(G) of a (multi)graph G with maximum degree ∆(G) and maximum multiplicity μ(G) satisfies ∆(G) ≤ χ(G) ≤ ∆(G) + μ(G), and Holyer’s Theorem [I… CONTINUE READING