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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Bibliographic Details
Published inRandom structures & algorithms Vol. 57; no. 3; pp. 730 - 744
Main Authors Davies, Ewan, Joannis de Verclos, Rémi, Kang, Ross J., Pirot, François
Format Journal Article
LanguageEnglish
Published New York John Wiley & Sons, Inc 01.10.2020
Wiley Subscription Services, Inc
Wiley
Subjects
Apexes
Coloring
Combinatorics
Computer Science
Discrete Mathematics
Graphs
hard‐core model
list coloring
Mathematics
triangle‐free graphs
hard‐core model
list coloring
triangle‐free graphs
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Summary: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.
Bibliography:Funding information
This research was supported by the European Research Council under the European Union's Seventh Framework Programme, FP7/2007‐2013, European Research Council, Nederlandse Organisatie voor Wetenschappelijk Onderzoek, ERC Grant, 339109 (E. D.), Vidi Grant of the Netherlands Organisation for Scientific Research (NWO), 639.032.614 (R. J. V.) and (R. J. K.)
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Funding information This research was supported by the European Research Council under the European Union's Seventh Framework Programme, FP7/2007‐2013, European Research Council, Nederlandse Organisatie voor Wetenschappelijk Onderzoek, ERC Grant, 339109 (E. D.), Vidi Grant of the Netherlands Organisation for Scientific Research (NWO), 639.032.614 (R. J. V.) and (R. J. K.)
ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.20945