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arXiv · 2604.27690

Online Coloring for Graphs of Large Odd Girth

Hirotaka Yoneda·Masataka Yoneda
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Abstract

We study the problem of online coloring for graphs with large odd girth. The best previously known algorithm uses $O(n^{1/2})$ colors, which was discovered by Kierstead in 1998. This algorithm works when the odd girth is 7 or more. In this paper, we provide the following: for every $\varepsilon > 0$, there exists a constant $g' \in \{3, 5, 7, \dots\}$ such that graphs with odd girth at least $g'$ can be deterministically colored online using $O(n^{\varepsilon})$ colors.

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Hirotaka Yoneda, Masataka Yoneda. 2026-04-30. Online Coloring for Graphs of Large Odd Girth. https://arxiv.org/abs/2604.27690

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