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The Maximum Chromatic Index of Multigraphs with Given Δ and μ

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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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Authors and Affiliations

  1. Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada

    Diego Scheide

  2. Institute of Mathematics, Technische Universität Ilmenau, PF 100 565, 98684, Ilmenau, Germany

    Michael Stiebitz

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  1. Diego Scheide
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  2. Michael Stiebitz
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Correspondence to Michael Stiebitz.

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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

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