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Online Coloring for Graphs of Large Odd Girth

Authors Hirotaka Yoneda , Masataka Yoneda

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LIPIcs.ESA.2026.127.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph coloring
  • Theory of computation → Online algorithms
Keywords
  • online coloring
  • online algorithms
  • graph theory
  • graph coloring
  • odd girth

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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 ε > 0, there exists a constant g' ∈ {3, 5, 7, …} such that graphs with odd girth at least g' can be deterministically colored online using O(n^ε) colors.

Cite As Get BibTex

Hirotaka Yoneda and Masataka Yoneda. Online Coloring for Graphs of Large Odd Girth. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 127:1-127:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.127

Author Details

Hirotaka Yoneda
  • The University of Tokyo, Japan
Masataka Yoneda
  • The University of Tokyo, Japan

Funding

  • Yoneda, Hirotaka: Supported by JSPS JP25K24465, JST ASPIRE JPMJAP2302, and JST ACT-X JPMJAX25CT.
  • Yoneda, Masataka: Supported by JSPS JP25K24465 and JST ASPIRE JPMJAP2302.

Acknowledgements

We are grateful to our professor Ken-ichi Kawarabayashi for helpful discussions and comments.

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