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Edge-Coloring Sparse Graphs with Δ Colors in Quasilinear Time

Author Łukasz Kowalik

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  • Mathematics of computing → Graph coloring
  • Theory of computation → Graph algorithms analysis
Keywords
  • edge coloring
  • algorithm
  • sparse
  • graph
  • quasilinear

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Abstract

In this paper we show that every graph G of bounded maximum average degree mad(G) and with maximum degree Δ can be edge-colored using the optimal number of Δ colors in quasilinear time, whenever Δ ≥ 2mad(G). The maximum average degree is within a multiplicative constant of other popular graph sparsity parameters like arboricity, degeneracy or maximum density. Our algorithm extends previous results of Chrobak and Nishizeki [Marek Chrobak and Takao Nishizeki, 1990] and Bhattacharya, Costa, Panski and Solomon [Sayan Bhattacharya et al., 2023].

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Łukasz Kowalik. Edge-Coloring Sparse Graphs with Δ Colors in Quasilinear Time. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 81:1-81:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ESA.2024.81

Author Details

Łukasz Kowalik
  • Institute of Informatics, University of Warsaw, Poland

Funding

This work is a part of project BOBR that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 948057).

Acknowledgements

The author wishes to thank Bartłomiej Bosek, Jadwiga Czyżewska, Konrad Majewski and Anna Zych-Pawlewicz for helpful discussions on related topics. The author is also grateful to the reviewers for helpful comments.

References

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