All graphs are majority 3-choosable
Jan Ouborny, Max Pitz
TL;DR
This paper proves that every graph can be colored with three choices in a majority sense, extending previous results and confirming a recent conjecture in graph theory.
Contribution
It establishes that all graphs are majority 3-choosable, generalizing prior work and confirming a conjecture by Haslegrave from 2020.
Findings
Every graph is majority 3-choosable.
Generalizes Shelah-Milner's result on unfriendly 3-partitions.
Confirms Haslegrave's conjecture from 2020.
Abstract
Every graph is majority 3-choosable. This generalises the result by Shelah-Milner that every graph has an unfriendly 3-partition, confirming a conjecture of Haslegrave from 2020.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Graph Theory Research · Limits and Structures in Graph Theory