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Article Dans Une Revue Random Structures and Algorithms Année : 2020

Coloring triangle‐free graphs with local list sizes

Résumé

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.
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Dates et versions

hal-04245511 , version 1 (12-01-2024)

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Ewan Davies, Rémi de Joannis de Verclos, Ross Kang, François Pirot. Coloring triangle‐free graphs with local list sizes. Random Structures and Algorithms, 2020, 57 (3), pp.730-744. ⟨10.1002/rsa.20945⟩. ⟨hal-04245511⟩
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