2021/12/19 by Mafi, Amir, Naderi, Dler
#13C05 #13C14 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2112.10062
In this paper we study almost Cohen-Macaulay bipartite graphs. Furthermore, we prove that if G is almost Cohen-Macaulay bipartite graph with at least one vertex of positive degree, then there is a vertex of °(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.