2026-07-20T15:08:09Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:26193 2026-07-02T07:14:09Z ddc:004 open_access

The Planar Edge-Coloring Theorem of Vizing in O(nlog n) Time Jędrzejczak, Patryk Kowalik, Łukasz edge coloring algorithm planar graph Vizing quasilinear In 1965, Vizing [Vadim G. Vizing, 1965] showed that every planar graph of maximum degree Δ ≥ 8 can be edge-colored using Δ colors. The direct implementation of Vizing’s proof gives an algorithm that finds the coloring in O(n²) time for an n-vertex input graph. Chrobak and Nishizeki [Marek Chrobak and Takao Nishizeki, 1990] have shown a more careful algorithm, which improves the time to O(nlog n), though only for Δ ≥ 9. In this paper, we extend their ideas to get an algorithm also for the missing case Δ = 8. To this end, we modify the original recoloring procedure of Vizing. This generalizes to bounded genus graphs of maximum degree 8 in the sense that in time O(nlog n) the algorithm colors the graph using the optimal number of colors which may be 9 for relatively small graphs. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Patryk Jędrzejczak and Łukasz Kowalik 2026 Is Part Of LIPIcs, Volume 376, 52nd International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.WG.2026.27 urn:nbn:de:0030-drops-261931 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WG.2026.27 eng https://creativecommons.org/licenses/by/4.0/legalcode