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Coloring triangle‐free graphs with local list sizes

We prove two distinct and natural refinements of a recent breakthrough result of Molloy (and a follow‐up work of Bernshteyn) on the (list) chromatic number of triangle‐free graphs. In both our results, we permit the amount of color made available to vertices of lower degree to be accordingly lower....

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Detalles Bibliográficos
Autores principales: Davies, Ewan, de Joannis de Verclos, Rémi, Kang, Ross J., Pirot, François
Formato: Online Artículo Texto
Lenguaje:English
Publicado: John Wiley & Sons, Inc. 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7508179/
https://www.ncbi.nlm.nih.gov/pubmed/32999582
http://dx.doi.org/10.1002/rsa.20945
Descripción
Sumario:We prove two distinct and natural refinements of a recent breakthrough result of Molloy (and a follow‐up work of Bernshteyn) on the (list) chromatic number of triangle‐free graphs. In both our results, we permit the amount of color made available to vertices of lower degree to be accordingly lower. One result concerns list coloring and correspondence coloring, while the other concerns fractional coloring. Our proof of the second illustrates the use of the hard‐core model to prove a Johansson‐type result, which may be of independent interest.