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arXiv · 2112.10062

Almost Cohen-Macaulay bipartite graphs and connected in codimension two

Amir Mafi·Dler Naderi
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Abstract

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 $\deg(v) \leq 2$. 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 $G\setminus\{v\}$ 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.

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Amir Mafi, Dler Naderi. 2021-12-19. Almost Cohen-Macaulay bipartite graphs and connected in codimension two. https://arxiv.org/abs/2112.10062

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