Year: 2026
Type: preprint
Abstract: A circular $r$-coloring of a signed graph maps its vertices to a circle of circumference $r\ge2$, with the endpoints of negative edges at circular distance at least $1$ and those of positive edges at most $r/2-1$; the circular chromatic number is the infimum of such $r$. We construct a simple planar signed triangulation on $85$ vertices with circular chromatic number exactly $5$. This improves the lower bound on the supremum of the circular chromatic numbers of simple planar signed graphs from $14/3$ to $5$, giving a partial answer to a question posed by Naserasr, Wang, and Zhu.
Source: arXiv (Cornell University)
Authors: Wang, Lujia, Zhou, Huan
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G1931219828
OpenAlex ID: W7223927153