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Resolution and Betti numbers of Vertex cover ideals

2024/04/01 by Hà, Tài Huy, Hibi, Takayuki
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.01001

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 βi,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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