The ∘ operation and * operation of Cohen-Macaulay bipartite graphs

Yulong Yang; Guangjun Zhu; Yijun Cui; Shiya Duan

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 3, page 735-757
  • ISSN: 0011-4642

Abstract

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Let G be a finite simple graph with the vertex set V and let I G be its edge ideal in the polynomial ring S = 𝕂 [ V ] . We compute the depth and the Castelnuovo-Mumford regularity of S / I G when G = G 1 ∘ G 2 or G = G 1 * G 2 is a graph obtained from Cohen-Macaulay bipartite graphs G 1 , G 2 by the ∘ operation or * operation, respectively.

How to cite

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Yang, Yulong, et al. "The $\circ $ operation and $*$ operation of Cohen-Macaulay bipartite graphs." Czechoslovak Mathematical Journal 74.3 (2024): 735-757. <http://eudml.org/doc/299300>.

@article{Yang2024,
abstract = {Let $G$ be a finite simple graph with the vertex set $V$ and let $I_G$ be its edge ideal in the polynomial ring $S= \mathbb \{K\} [V]$. We compute the depth and the Castelnuovo-Mumford regularity of $S/I_G$ when $G=G_1\circ G_2$ or $G=G_1* G_2$ is a graph obtained from Cohen-Macaulay bipartite graphs $G_1$, $G_2$ by the $\circ $ operation or $*$ operation, respectively.},
author = {Yang, Yulong, Zhu, Guangjun, Cui, Yijun, Duan, Shiya},
journal = {Czechoslovak Mathematical Journal},
keywords = {regularity; depth; $\circ $ operation; $*$ operation; Cohen-Macaulay bipartite graph},
language = {eng},
number = {3},
pages = {735-757},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The $\circ $ operation and $*$ operation of Cohen-Macaulay bipartite graphs},
url = {http://eudml.org/doc/299300},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Yang, Yulong
AU - Zhu, Guangjun
AU - Cui, Yijun
AU - Duan, Shiya
TI - The $\circ $ operation and $*$ operation of Cohen-Macaulay bipartite graphs
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 3
SP - 735
EP - 757
AB - Let $G$ be a finite simple graph with the vertex set $V$ and let $I_G$ be its edge ideal in the polynomial ring $S= \mathbb {K} [V]$. We compute the depth and the Castelnuovo-Mumford regularity of $S/I_G$ when $G=G_1\circ G_2$ or $G=G_1* G_2$ is a graph obtained from Cohen-Macaulay bipartite graphs $G_1$, $G_2$ by the $\circ $ operation or $*$ operation, respectively.
LA - eng
KW - regularity; depth; $\circ $ operation; $*$ operation; Cohen-Macaulay bipartite graph
UR - http://eudml.org/doc/299300
ER -

References

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