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Arboricity-Dependent Algorithms for Edge Coloring

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

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Author Details

Sayan Bhattacharya
  • University of Warwick, UK
Martín Costa
  • University of Warwick, UK
Nadav Panski
  • Tel Aviv University, Israel
Shay Solomon
  • Tel Aviv University, Israel

Funding

Shay Solomon is funded by the European Union (ERC, DynOpt, 101043159). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. Shay Solomon and Nadav Panski are supported by the Israel Science Foundation (ISF) grant No.1991/1. Shay Solomon is also supported by a grant from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel, and the United States National Science Foundation (NSF).

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.SWAT.2024.12

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic graph algorithms
Keywords
  • Dynamic Algorithms
  • Graph Algorithms
  • Edge Coloring
  • Arboricity

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References

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