The role of the Axiom of Choice in proper and distinguishing colourings

DOI10.26493/1855-3974.2863.4b9OpenAlexW3110046977MaRDI QIDQ5881017

Marcin Stawiski

Publication date: 9 March 2023

Published in: Ars Mathematica Contemporanea (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.00141

zbMATH Keywords

infinite graphsgraph automorphismsAxiom of Choiceproper colouringsasymmetric colouringsdistinguishing colourings

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Structural characterization of families of graphs (05C75) Coloring of graphs and hypergraphs (05C15) Axiom of choice and related propositions (03E25) Infinite graphs (05C63)

Cites Work

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• Distinguishing graphs by edge-colourings
• Graph colorings and the axiom of choice
• A generalisation of a theorem of de Bruijn and Erdős on the chromatic numbers of infinite graphs
• Asymmetric trees with two prescribed degrees
• Set Theory
• The optimal general upper bound for the distinguishing index of infinite graphs
• Axiom of choice
• Distinguishing infinite graphs with bounded degrees

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