New Bounds for Facial Nonrepetitive Colouring
Prosenjit Bose, Vida Dujmovi\'c, Pat Morin, and Lucas Rioux-Maldague
TL;DR
This paper establishes new upper bounds for the facial nonrepetitive chromatic number in outerplanar and planar graphs, advancing understanding of graph coloring constraints.
Contribution
It provides the first proven bounds for facial nonrepetitive coloring in these classes of graphs, improving previous theoretical limits.
Findings
Outerplanar graphs have a facial nonrepetitive chromatic number at most 11.
Planar graphs have a facial nonrepetitive chromatic number at most 22.
These bounds are the first proven limits for these graph classes.
Abstract
We prove that the facial nonrepetitive chromatic number of any outerplanar graph is at most 11 and of any planar graph is at most 22.
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