Odd colouring on the torus

2022/05/09 by Harry Metrebian, Metrebian, Harry · 1 citation
Computer Science · Mathematics · #05C15 (Primary) 05C10 (Secondary) #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2205.04398

openalex publication_date 2022/05/09 · openalex created_date 2022/05/22 · openalex updated_date 2026/07/28

Abstract

A proper vertex-colouring of a simple graph G is said to be odd if, for every non-isolated vertex v of G, some colour appears an odd number of times in the neighbourhood of v. We show that if G embeds in the torus, then it admits a proper odd vertex-colouring with at most 9 colours.

Cited by

• Odd list-coloring of graphs of small Euler genus with no short cycles of specific types

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