Faster Vizing and near-Vizing edge coloring algorithms

S Assadi - Proceedings of the 2025 Annual ACM-SIAM …, 2025 - SIAM
Vizing's celebrated theorem states that every simple graph with maximum degree Δ admits a
(Δ+ 1) edge coloring which can be found in O (m· n) time on n-vertex m-edge graphs. This is …

Online Dependent Rounding Schemes for Bipartite Matchings, with

J Naor, A Srinivasan, D Wajc - Proceedings of the 2025 Annual ACM-SIAM …, 2025 - SIAM
We introduce the abstract problem of rounding an unknown fractional bipartite b-matching x
revealed online (eg, output by an online fractional algorithm), exposed node-by-node on …

Randomized greedy online edge coloring succeeds for dense and randomly-ordered graphs

A Dudeja, R Goswami, M Saks - Proceedings of the 2025 Annual ACM-SIAM …, 2025 - SIAM
Vizing's theorem states that any graph of maximum degree Δ can be properly edge colored
with at most Δ+ 1 colors. In the online setting, it has been a matter of interest to find an …

Streaming edge coloring with asymptotically optimal colors

M Saneian, S Behnezhad - 51st International Colloquium on …, 2024 - drops.dagstuhl.de
Given a graph G, an edge-coloring is an assignment of colors to edges of G such that any
two edges sharing an endpoint receive different colors. By Vizing's celebrated theorem, any …

Streaming edge coloring with asymptotically optimal colors

S Behnezhad, M Saneian - arXiv preprint arXiv:2305.01714, 2023 - arxiv.org
Given a graph $ G $, an edge-coloring is an assignment of colors to edges of $ G $ such that
any two edges sharing an endpoint receive different colors. By Vizing's celebrated theorem …

Deterministic Online Bipartite Edge Coloring

J Blikstad, O Svensson, R Vintan, D Wajc - … of the 2025 Annual ACM-SIAM …, 2025 - SIAM
We study online bipartite edge coloring, with nodes on one side of the graph revealed
sequentially. The trivial greedy algorithm is (2—o (1))-competitive, which is optimal for …

Even Faster (Δ+ 1)-Edge Coloring via Shorter Multi-Step Vizing Chains

S Bhattacharya, M Costa, S Solomon, T Zhang - Proceedings of the 2025 …, 2025 - SIAM
Vizing's Theorem from 1964 states that any n-vertex m-edge graph with maximum degree Δ
can be edge colored using at most Δ+ 1 colors. For over 40 years, the state-of-the-art …

Nibbling at long cycles: Dynamic (and static) edge coloring in optimal time

S Bhattacharya, M Costa, N Panski, S Solomon - Proceedings of the 2024 …, 2024 - SIAM
We consider the problem of maintaining a (1+ ɛ)∆-edge coloring in a dynamic graph G with
n nodes and maximum degree at most Δ. The state-of-the-art update time is O ɛ (polylog …

Low-memory algorithms for online and w-streaming edge coloring

P Ghosh, M Stoeckl - arXiv preprint arXiv:2304.12285, 2023 - arxiv.org
For edge coloring, the online and the W-streaming models seem somewhat orthogonal: the
former needs edges to be assigned colors immediately after insertion, typically without any …

Streaming edge coloring with subquadratic palette size

S Chechik, D Mukhtar, T Zhang - arXiv preprint arXiv:2305.07090, 2023 - arxiv.org
In this paper, we study the problem of computing an edge-coloring in the (one-pass) W-
streaming model. In this setting, the edges of an $ n $-node graph arrive in an arbitrary order …