@inproceedings{6fc79f15a21f4d2d8c4b551acd1d5f4e,
title = "Faster (Δ+1)-Edge Coloring: Breaking the m√n Time Barrier",
abstract = "Vizing's theorem states that any n-vertex m-edge graph of maximum degree Δ can be edge colored using at most Δ+1 different colors [Diskret. Analiz, '64]. Vizing's original proof is algorithmic and shows that such an edge coloring can be found in {\~O}(mn) time. This was subsequently improved to {\~O}(m√n), independently by Arjomandi [1982] and by Gabow et al. [1985]. In this paper we present an algorithm that computes such an edge coloring in {\~O}(mn1/3), time, giving the first polynomial improvement for this fundamental problem in over 40 years.",
keywords = "Vizing's theo-rem, edge coloring, graph algorithms",
author = "Sayan Bhattacharya and Din Carmon and Martin Costa and Shay Solomon and Tianyi Zhang",
note = "Publisher Copyright: {\textcopyright} 2024 IEEE.; 65th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2024 ; Conference date: 27-10-2024 Through 30-10-2024",
year = "2024",
month = jan,
day = "1",
doi = "10.1109/FOCS61266.2024.00128",
language = "English",
series = "Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS",
publisher = "IEEE Computer Society",
pages = "2186--2201",
booktitle = "Proceedings - 2024 IEEE 65th Annual Symposium on Foundations of Computer Science, FOCS 2024",
address = "United States",
}