English

Almost Cohen-Macaulay bipartite graphs and connected in codimension two

Commutative Algebra 2021-12-21 v1 Combinatorics

Abstract

In this paper we study almost Cohen-Macaulay bipartite graphs. Furthermore, we prove that if GG is almost Cohen-Macaulay bipartite graph with at least one vertex of positive degree, then there is a vertex of deg(v)2\deg(v) \leq 2. In particular, if GG is an almost Cohen-Macaulay bipartite graph and uu is a vertex of degree one of GG and vv its adjacent vertex, then G{v}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.

Keywords

Cite

@article{arxiv.2112.10062,
  title  = {Almost Cohen-Macaulay bipartite graphs and connected in codimension two},
  author = {Amir Mafi and Dler Naderi},
  journal= {arXiv preprint arXiv:2112.10062},
  year   = {2021}
}

Comments

12 pages. Comments welcome

R2 v1 2026-06-24T08:23:24.142Z