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].
@InProceedings{kowalik:LIPIcs.ESA.2024.81, author = {Kowalik, {\L}ukasz}, title = {{Edge-Coloring Sparse Graphs with \Delta Colors in Quasilinear Time}}, booktitle = {32nd Annual European Symposium on Algorithms (ESA 2024)}, pages = {81:1--81:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-338-6}, ISSN = {1868-8969}, year = {2024}, volume = {308}, editor = {Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.81}, URN = {urn:nbn:de:0030-drops-211523}, doi = {10.4230/LIPIcs.ESA.2024.81}, annote = {Keywords: edge coloring, algorithm, sparse, graph, quasilinear} }
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