Non-vanishingness of Betti numbers of edge ideals

Details Non-vanishingness of Betti numbers of edge ideals Non-vanishingness of Betti numbers of edge ideals

2011-10-11

arxiv.org/abs/1110.2333v3

Mathematics

Commutative Algebra

12 pages. v2: Since Corollary 5.6 was proved by S. Morey and R. H. Villarreal, we added the reference; v3: We changed the expl

Scientific paper

Given finite simple graph one can associate the edge ideal. In this paper we discuss the non-vanishingness of the graded Betti numbers of edge ideals in terms of the original graph. In particular, we give a necessary and sufficient condition for a chordal graph on which the graded Betti number does not vanish and characterize the graded Betti number for a forest. Moreover we characterize the projective dimension for a chordal graph.

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