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arXiv · 2607.09631

Cut-homotopies and the complexity of edge-coloring problems

Alexey Barsukov·Roman Feller·Maximilian Hadek·Davide Perinti
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Abstract

We study the computational complexity of problems that ask if a given graph admits an edge-coloring that does not contain an edge-colored clique from some fixed finite family. We show that every such problem is poly-time equivalent to a Constraint Satisfaction Problem, yielding a P vs. NP-complete dichotomy. Our main contribution lies in the reduction from the CSP to the coloring problem where we apply methods from Ramsey theory and a novel notion of cut-homotopy.

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Alexey Barsukov, Roman Feller, Maximilian Hadek, Davide Perinti. 2026-07-10. Cut-homotopies and the complexity of edge-coloring problems. https://arxiv.org/abs/2607.09631

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