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arXiv · 2606.26689

An algebraic study of ideals of weak graph homomorphisms

Francesco Navarra·Ayesha Asloob Qureshi·Seyed Amin Seyed Fakhari
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Abstract

Let $G$ and $H$ be finite simple graphs and assume that either both are undirected or both are directed. We introduce and study the ideal of weak graph homomorphisms $I_{G\to H}$. We characterize all graphs $G$ and $H$ for which every (equivalently, some) power of $I_{G\to H}$ has a linear resolution. Moreover, unmixedness, Cohen-Macaulayness, projective dimension and Castelnuovo-Mumford regularity of these ideals are studied.

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Francesco Navarra, Ayesha Asloob Qureshi, Seyed Amin Seyed Fakhari. 2026-06-25. An algebraic study of ideals of weak graph homomorphisms. https://arxiv.org/abs/2606.26689

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