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All graphs are majority 3-choosable

Jan Ouborny, Max Pitz

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.

All graphs are majority 3-choosable

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.
Paper Structure (3 sections, 7 theorems, 16 equations, 2 figures)

This paper contains 3 sections, 7 theorems, 16 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The countable case
  3. The uncountable case

Key Result

Theorem 1

Every graph is majority $3$-choosable.

Figures (2)

  • Figure 1: The construction
  • Figure 2: Case 1

Theorems & Definitions (20)

  • Theorem 1
  • Theorem 2
  • Lemma 2.1
  • proof
  • proof : Proof of Theorem \ref{['thm_intro2']} for countable $B$
  • Lemma 3.1: shelah1990graphs
  • proof
  • Lemma 3.2: Saturation lemma
  • proof
  • Proposition 3.3
  • ...and 10 more