The Taub Faculty of Computer Science Events and Talks

Vizing’s Theorem provides an algorithm that edge colors any graph of maximum degree Δ using Δ+1 colors, which is necessary for some graphs, and at most one higher than necessary for any graph. In online settings, the trivial greedy algorithm requires 2Δ-1 colors, and Bar-Noy, Motwani and Naor in the early 90s showed that this is best possible, at least in the low-degree regime. In contrast, they conjectured that for graphs of superlogarithmic-in-n maximum degree, much better can be done, and that even (1+o(1))Δ-colors suffice online. In this talk I will outline the history of this conjecture, and its recent resolution, together with extensions of a flavor resembling classic and recent results on *list* edge-coloring and “local” edge-coloring. Talk based in part on joint works with many wonderful and colorful collaborators, including Sayan Bhattacharya, Joakim Blikstad, Ilan R. Cohen, Fabrizio Grandoni, Seffi Naor, Binghui Peng, Amin Saberi, Aravind Srinivasan, Ola Svensson and Radu Vintan.