A generalization of Eagon–Reiner’s theorem and a characterization of bi-CM_t bipartite and chordal graphs

ABSTRACT

We give a generalization of Eagon-Reiner’s theorem relating Betti numbers of the Stanley-Reisner ideal of a simplicial complex and the CM_t property of its Alexander dual. Then we characterize bi-CM_t bipartite graphs and bi-CM_t chordal graphs. These are generalizations of recent results due to Herzog and Rahimi.

KEYWORDS:

• Bipartite graph
• chordal graph
• Cohen–Macaulay complex
• CM_t complex
• Eagon–Reiner theorem

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 13H10
• 13F55

Acknowledgments

The authors thank Rashid Zaare-Nahandi for bringing attention to [4]. They also wish to thank Jürgen Herzog for suggesting them to arrange the Betti diagrams in the present form using the notation due to Macaulay. They are grateful to the reviewer for a careful reading of the paper and for valuable suggestions and comments.