Local version of Vizing's theorem for multi-graphs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914779662123008 |
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| author | Conley, Clinton T. Grebik, Jan Pikhurko, Oleg |
| author_facet | Conley, Clinton T. Grebik, Jan Pikhurko, Oleg |
| contents | Extending a result of Christiansen, we prove that every mutli-graph $G=(V,E)$ admits a proper edge colouring $ϕ:E\to \{1,2,\dots\}$ which is local, that is, $ϕ(e)\le \max\{d(x)+π(x),d(y)+π(y)\}$ for every edge $e$ with end-points $x,y\in V$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_04173 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Local version of Vizing's theorem for multi-graphs Conley, Clinton T. Grebik, Jan Pikhurko, Oleg Combinatorics Extending a result of Christiansen, we prove that every mutli-graph $G=(V,E)$ admits a proper edge colouring $ϕ:E\to \{1,2,\dots\}$ which is local, that is, $ϕ(e)\le \max\{d(x)+π(x),d(y)+π(y)\}$ for every edge $e$ with end-points $x,y\in V$, 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. |
| title | Local version of Vizing's theorem for multi-graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2306.04173 |