TCS+ talk: Wednesday, December 4, Martín Costa, University of Warwick
Clement Canonne
Our next talk (the last of 2024!) will take place this coming Wednesday, December 4th at 10:30 AM Eastern Time (7:30 AM Pacific Time, 16:30 Central European Time, 15:30 UTC -- note the unusual time!). Martín Costa from the University of Warwick will speak about "Vizing's Theorem in Near-Linear Time" (abstract below).
Please sign up on the online form at https://sites.google.com/view/tcsplus/welcome/next-tcs-talk if you wish to join the talk as an individual or a group. Registration is /not/ required to attend the interactive talk, and the link will be posted on the website the day prior to the talk; however, by registering in the form, you will receive a reminder, along with the link. (The link to the recording will also be posted on our website afterwards.)
Hoping to see you all there,
The organizers
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Speaker: Martín Costa (University of Warwick)
Title: Vizing's Theorem in Near-Linear Time
Abstract: Vizing's theorem states that any $n$-vertex $m$-edge graph of maximum degree $\Delta$ can be edge colored using at most $\Delta + 1$ different colors [Vizing, 1964]. Vizing's original proof is algorithmic and shows that such an edge coloring can be found in $O(mn)$ time. This was improved to $\tilde O(m\sqrt{n})$ time, independently by [Arjomandi, 1982] and by [Gabow et al., 1985].
Very recently, independently and concurrently, this runtime bound was further improved to $\tilde{O}(n^2)$ by [Assadi, 2024] and $\tilde O(mn^{1/3})$ by [Bhattacharya, Carmon, Costa, Solomon and Zhang, 2024] (and subsequently to $\tilde O(mn^{1/4})$ time by [Bhattacharya, Costa, Solomon and Zhang, 2024]).
In this talk, we present an algorithm that computes a $(\Delta+1)$-edge coloring in near-linear time -- in fact, only $O(m\log{\Delta})$ time -- giving a near-optimal algorithm for this fundamental problem.