Non-vanishingness of Betti numbers of edge ideals

By K. Kimura. 2011

51 citations recorded by the source corpus.

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.

View Paper: https://www.semanticscholar.org/paper/8265d17aee4772e43cc5cfabbae7bf077549e20f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Adam Van Tuyl
2. Huy Tài Hà
3. Russ Woodroofe
4. K. Kimura

Citations in the corpus

• A Beginner’s Guide to Edge and Cover Ideals (2013, methodology): “Hibi, Kimura, and Murai where then able to exploit this formula in their study of f -vectors (see [39]); this formula was also used by Kimura [45].”