Almost Cohen–Macaulay bipartite graphs and connected in codimension two.

In this paper, we study almost Cohen–Macaulay bipartite graphs. In particular, we prove that if G is an almost Cohen–Macaulay bipartite graph with at least one vertex of positive degree, then there is a vertex of deg(v) ≤ 2. In particular, if G is an almost Cohen–Macaulay bipartite graph and u is a vertex of degree one of G and v its adjacent vertex, then G∖{v} is almost Cohen–Macaulay. Also, we show that an unmixed Ferrers graph is almost Cohen–Macaulay if and only if it is connected in codimension two. Moreover, we give some examples. [ABSTRACT FROM AUTHOR]