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arXiv · 2404.01001

Resolution and Betti numbers of Vertex cover ideals

Tài Huy Hà·Takayuki Hibi
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Abstract

The vertex cover ideal $J(G)$ of a finite graph $G$ is studied. We characterize when a Cohen--Macaulay vertex cover ideal $J(G)$ has a Scarf minimal free resolution. Furthermore, by using both combinatorial and topological techniques, the graded Betti number $\beta_{i,i+j}(J(G))$, where $i$ and $j$ are the projective dimension and the regularity of $J(G)$, is computed, when $G$ is either a path or a cycle.

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Tài Huy Hà, Takayuki Hibi. 2024-04-01. Resolution and Betti numbers of Vertex cover ideals. https://arxiv.org/abs/2404.01001

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