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Local version of Vizing's theorem for multi-graphs
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Conley, C. T., Grebik, J. and Pikhurko, Oleg (2024) Local version of Vizing's theorem for multi-graphs. Journal of Graph Theory . ISSN 0364-9024. (In Press)
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Abstract
Extending a result of Christiansen, we prove that every mutli-graph G = (V, E) admits a proper edge colouring φ : E → {1, 2, . . . } which is local, that is, φ(e) 6 max{d(x) + π(x), d(y) + π(y)} for every edge e with end-points x, y ∈ V , where d(z) (resp. π(z)) denotes the degree of a vertex z (resp. the maximum edge multiplicity at z). This is derived from a
local version of the Fan Equation
Item Type: | Journal Article | ||||||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Journal or Publication Title: | Journal of Graph Theory | ||||||||||||
Publisher: | John Wiley & Sons Ltd. | ||||||||||||
ISSN: | 0364-9024 | ||||||||||||
Official Date: | 2024 | ||||||||||||
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Status: | Peer Reviewed | ||||||||||||
Publication Status: | In Press | ||||||||||||
Re-use Statement: | This is the peer reviewed version of the following article: [FULL CITE], which has been published in final form at [Link to final article using the DOI]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited. | ||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
Date of first compliant deposit: | 2 May 2024 | ||||||||||||
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