Abstract
Let f(Δ, μ) = max {χ′(G) | Δ (G) = Δ, μ(G) = μ} where χ′(G), Δ(G) and μ(G) denote the the chromatic index, the maximum degree and the maximum multiplicity of the multigraph G, respectively. If Δ < 2μ, then Shannon’s bound implies that the gap between f(Δ, μ) and Vizing’s bound Δ + μ can be arbitrarily large. In this note, we prove that this is also the case for Δ ≥ 2μ (see Theorem 4).
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Scheide, D., Stiebitz, M. The Maximum Chromatic Index of Multigraphs with Given Δ and μ . Graphs and Combinatorics 28, 717–722 (2012). https://doi.org/10.1007/s00373-011-1068-4
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DOI: https://doi.org/10.1007/s00373-011-1068-4