Bi-Cohen-Macaulay graphs

Jürgen Herzog, Ahad Rahimi


In this paper we consider bi-Cohen-Macaulay graphs, and give a complete classification of such graphs in the case they are bipartite or chordal. General bi-Cohen-Macaulay graphs are classified up to separation. The inseparable bi-Cohen-Macaulay graphs are determined. We establish a bijection between the set of all trees and the set of inseparable bi-Cohen-Macaulay graphs.


Bi-Cohen-Macaulay, Bipartite and chordal graphs, Generic graphs, Inseparability

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