Arboricity-Dependent Algorithms for Edge Coloring

Published: 01 Jan 2024, Last Modified: 13 May 2025SWAT 2024EveryoneRevisionsBibTeXCC BY-SA 4.0
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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