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Coloring graphs by translates in the circle

Author
Candela, Pablo; Catalá, Carlos; Hancock, Robert; Kabela, Adam; Král, Daniel; Lamaison, Ander; Vena, Lluís
Entity
UAM. Departamento de Matemáticas
Publisher
Elsevier
Date
2021-04-27
Citation
10.1016/j.ejc.2021.103346
European Journal of Combinatorics 96 (2021): 103346
 
 
 
ISSN
0195-6698 (print)
DOI
10.1016/j.ejc.2021.103346
Funded by
The first author was supported by the Spanish Ministerio de Economía y Competitividad project MTM2017-83496-P. The third, fourth and fifth authors were supported by the MUNI Award in Science and Humanities of the Grant Agency of Masaryk University. The sixth author was supported by the German Research Foundation under Germany’s Excellence Strategy - MATH+ (EXC-2046/1, project ID: 390685689). The seventh author was supported by project 18-13685Y of the Czech Science Foundation (GACR)
Project
Gobierno de España. MTM2017-83496-P
Editor's Version
https://doi.org/10.1016/j.ejc.2021.103346
Subjects
Circular chromatic numbers; Borel; Gyrochromatic number; Abelian groups; Matemáticas
URI
http://hdl.handle.net/10486/700425
Rights
© 2021 Elsevier Ltd.

Licencia de Creative Commons
Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Abstract

The fractional and circular chromatic numbers are the two most studied non-integral refinements of the chromatic number of a graph. Starting from the definition of a coloring base of a graph, which originated in work related to ergodic theory, we formalize the notion of a gyrocoloring of a graph: the vertices are colored by translates of a single Borel set in the circle group, and neighboring vertices receive disjoint translates. The corresponding gyrochromatic number of a graph always lies between the fractional chromatic number and the circular chromatic number. We investigate basic properties of gyrocolorings. In particular, we construct examples of graphs whose gyrochromatic number is strictly between the fractional chromatic number and the circular chromatic number. We also establish several equivalent definitions of the gyrochromatic number, including a version involving all finite abelian groups
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Google™ Scholar:Candela, Pablo - Catalá, Carlos - Hancock, Robert - Kabela, Adam - Král, Daniel - Lamaison, Ander - Vena, Lluís

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  • Producción científica en acceso abierto de la UAM [15086]

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