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DOI: 10.4230/LIPIcs.SWAT.2024.12
Arboricity-Dependent Algorithms for Edge Coloring

Authors: Sayan Bhattacharya, Martín Costa, Nadav Panski, and Shay Solomon

Published in: LIPIcs, Volume 294, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)

Abstract
The problem of edge coloring has been extensively studied over the years. Recently, this problem has received significant attention in the dynamic setting, where we are given a dynamic graph evolving via a sequence of edge insertions and deletions and our objective is to maintain an edge coloring of the graph. Currently, it is not known whether it is possible to maintain a (Δ + O(Δ^(1-μ)))-edge coloring in Õ(1) update time, for any constant μ > 0, where Δ is the maximum degree of the graph. In this paper, we show how to efficiently maintain a (Δ + O(α))-edge coloring in Õ(1) amortized update time, where α is the arboricty of the graph. Thus, we answer this question in the affirmative for graphs of sufficiently small arboricity.
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Sayan Bhattacharya, Martín Costa, Nadav Panski, and Shay Solomon. Arboricity-Dependent Algorithms for Edge Coloring. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bhattacharya_et_al:LIPIcs.SWAT.2024.12,
  author =	{Bhattacharya, Sayan and Costa, Mart{\'\i}n and Panski, Nadav and Solomon, Shay},
  title =	{{Arboricity-Dependent Algorithms for Edge Coloring}},
  booktitle =	{19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)},
  pages =	{12:1--12:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-318-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{294},
  editor =	{Bodlaender, Hans L.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2024.12},
  URN =		{urn:nbn:de:0030-drops-200524},
  doi =		{10.4230/LIPIcs.SWAT.2024.12},
  annote =	{Keywords: Dynamic Algorithms, Graph Algorithms, Edge Coloring, Arboricity}
}
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