Local version of Vizing's theorem for multigraphs-Reference-Cited by-同舟云学术

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Local version of Vizing's theorem for multigraphs

Published:2024-07-16 Issue: Volume: Page:
ISSN:0364-9024
Container-title:Journal of Graph Theory
language:en
Short-container-title:Journal of Graph Theory

Author:

Conley Clinton T.¹,Grebík Jan²³,Pikhurko Oleg⁴

Affiliation:

1. Department of Mathematical Sciences Carnegie Mellon University Pittsburgh Pennsylvania USA

2. Department of Mathematics, UCLA Los Angeles California USA

3. Faculty of Informatics Masaryk University Brno Czech Republic

4. Mathematics Institute and DIMAP, University of Warwick Coventry UK

Abstract

AbstractExtending a result of Christiansen, we prove that every multigraph admits a proper edge colouring which is local, that is, for every edge with end‐points , where (resp. ) denotes the degree of a vertex (resp. the maximum edge multiplicity at ). This is derived from a local version of the Fan Equation.

Publisher

Wiley

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/jgt.23155

Reference10 articles.

1. Edge-colouring graphs with local list sizes

2. List Edge and List Total Colourings of Multigraphs

3. The Power of Multi-step Vizing Chains

4. A. B. G.Christiansen The power of multi‐step Vizing chains E‐print arxiv:2210.07363 (2022).https://arxiv.org/abs/2210.07363

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