Coloring graphs by translates in the circle

J 2021

Coloring graphs by translates in the circle

CANDELA, Pablo, Carlos CATALÁ, Robert Arthur HANCOCK, Adam KABELA, Daniel KRÁĽ et. al.

Basic information

Original name

Coloring graphs by translates in the circle

Authors

CANDELA, Pablo, Carlos CATALÁ, Robert Arthur HANCOCK (826 United Kingdom of Great Britain and Northern Ireland, belonging to the institution), Adam KABELA (203 Czech Republic, belonging to the institution), Daniel KRÁĽ (203 Czech Republic, guarantor, belonging to the institution), Ander LAMAISON VIDARTE (724 Spain, belonging to the institution) and Lluís VENA

Edition

European Journal of Combinatorics, LONDON, ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 2021, 0195-6698

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 0.890

RIV identification code

RIV/00216224:14330/21:00124666

Organization unit

Faculty of Informatics

DOI

http://dx.doi.org/10.1016/j.ejc.2021.103346

UT WoS

000659230400014

Keywords in English

chromatic numbers

Abstract

V originále

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 & nbsp;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.

Links

MUNI/I/1677/2018, interní kód MU

Name: MUNI AWARD in Science and Humanitites 1 (Acronym: MASH 1)

Investor: Masaryk University, MASH - MUNI Award in Science and Humanities

Citovat

CANDELA, Pablo, Carlos CATALÁ, Robert Arthur HANCOCK, Adam KABELA, Daniel KRÁĽ, Ander LAMAISON VIDARTE and Lluís VENA. Coloring graphs by translates in the circle. European Journal of Combinatorics. LONDON: ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 2021, vol. 96, No 103346, p. 1-18. ISSN 0195-6698. Available from: https://dx.doi.org/10.1016/j.ejc.2021.103346.

@article{1824817,
   author = {Candela, Pablo and Catalá, Carlos and Hancock, Robert Arthur and Kabela, Adam and Kráľ, Daniel and Lamaison Vidarte, Ander and Vena, Lluís},
   article_location = {LONDON},
   article_number = {103346},
   doi = {http://dx.doi.org/10.1016/j.ejc.2021.103346},
   keywords = {chromatic numbers},
   language = {eng},
   issn = {0195-6698},
   journal = {European Journal of Combinatorics},
   title = {Coloring graphs by translates in the circle},
   url = {http://dx.doi.org/10.1016/j.ejc.2021.103346},
   volume = {96},
   year = {2021}
}

TY  - JOUR
ID  - 1824817
AU  - Candela, Pablo - Catalá, Carlos - Hancock, Robert Arthur - Kabela, Adam - Kráľ, Daniel - Lamaison Vidarte, Ander - Vena, Lluís
PY  - 2021
TI  - Coloring graphs by translates in the circle
JF  - European Journal of Combinatorics
VL  - 96
IS  - 103346
SP  - 1-18
EP  - 1-18
PB  - ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
SN  - 01956698
KW  - chromatic numbers
UR  - http://dx.doi.org/10.1016/j.ejc.2021.103346
N2  - 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 & nbsp;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.
ER  -

CANDELA, Pablo, Carlos CATALÁ, Robert Arthur HANCOCK, Adam KABELA, Daniel KRÁĽ, Ander LAMAISON VIDARTE and Lluís VENA. Coloring graphs by translates in the circle. \textit{European Journal of Combinatorics}. LONDON: ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 2021, vol.~96, No~103346, p.~1-18. ISSN~0195-6698. Available from: https://dx.doi.org/10.1016/j.ejc.2021.103346.

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