Faster algorithms for graph homomorphism via tractable constraint satisfaction

Clément Carbonnel

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arXiv · 2602.23000

Faster algorithms for graph homomorphism via tractable constraint satisfaction

Clément Carbonnel

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Abstract

We show that the existence of a homomorphism from an $n$-vertex graph $G$ to an $h$-vertex graph $H$ can be decided in time $2^{O(n)}h^{O(1)}$ and polynomial space if $H$ comes from a family of graphs that excludes a topological minor. The algorithm is based on a reduction to a single-exponential number of constraint satisfaction problems over tractable languages and can handle cost minimization. We also present an improved randomized algorithm for the special case where the graph $H$ is an odd cycle.

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Clément Carbonnel. 2026-02-26. Faster algorithms for graph homomorphism via tractable constraint satisfaction. https://arxiv.org/abs/2602.23000

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