Higher-dimensional generalization of Youngs' theorem and circular colorings

2025/05/29 by Enami, Kengo, Matsushita, Takahiro · 1 citation
#05C15 (Primary) 05C10 (Secondary) #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.23562

Abstract

In 1996, Youngs proved that any quadrangulation of the real projective plane is not 3-chromatic. This result has been extended in various directions over the years, including to other non-orientable closed surfaces, higher-dimensional analogues of quadrangulations and circular colorings. In this paper, we provide a generalization which yields some of these extensions of Youngs' theorem.

Citations

• Colouring normal quadrangulations of projective spaces
• Hom complexes of graphs whose codomains are square-free
• Hedetniemi's conjecture and strongly multiplicative graphs
• Random runners are very lonely

Cited by

• Closed neighborhood complexes of graphs

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