Edge-colouring graphs with local list sizes
The famous List Colouring Conjecture from the 1970s states that for every graph G the chromatic index of G is equal to its list chromatic index. In 1996 in a seminal paper, Kahn proved that the List Colouring Conjecture holds asymptotically. Our main result is a local generalization of Kahn's t...
| Autores: | , , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2024 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/459279 |
| Acesso em linha: | https://hdl.handle.net/2117/459279 https://dx.doi.org/10.1016/j.jctb.2023.10.010 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Graph theory Edge-colouring List colouring List colouring conjecture Local list colouring Vizing's Theorem Grafs, Teoria de Classificació AMS::05 Combinatorics::05C Graph theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
| Resumo: | The famous List Colouring Conjecture from the 1970s states that for every graph G the chromatic index of G is equal to its list chromatic index. In 1996 in a seminal paper, Kahn proved that the List Colouring Conjecture holds asymptotically. Our main result is a local generalization of Kahn's theorem. More precisely, we show that, for a graph G with sufficiently large maximum degree ¿ and minimum degree , the following holds: for every assignment L of lists of colours to the edges of G, such that for each edge , there is an L-edge-colouring of G. Furthermore, Kahn showed that the List Colouring Conjecture holds asymptotically for linear, k-uniform hypergraphs, and recently Molloy generalized Kahn's original result to correspondence colouring as well as its hypergraph generalization. We prove local versions of all of these generalizations by showing a weighted version that simultaneously implies all of our results. |
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