Computer Science > Data Structures and Algorithms
[Submitted on 24 May 2024]
Title:Faster $(Δ+ 1)$-Edge Coloring: Breaking the $m \sqrt{n}$ Time Barrier
View PDF HTML (experimental)Abstract:Vizing's theorem states that any $n$-vertex $m$-edge graph of maximum degree $\Delta$ can be {\em edge colored} using at most $\Delta + 1$ different colors [Diskret.~Analiz, '64]. Vizing's original proof is algorithmic and shows that such an edge coloring can be found in $\tilde{O}(mn)$ time. This was subsequently improved to $\tilde O(m\sqrt{n})$, independently by Arjomandi [1982] and by Gabow et al.~[1985].
In this paper we present an algorithm that computes such an edge coloring in $\tilde O(mn^{1/3})$ time, giving the first polynomial improvement for this fundamental problem in over 40 years.
References & Citations
Bookmark
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.