Sequentially Cohen-Macaulay binomial edge ideals
Ernesto Lax, Giancarlo Rinaldo, Francesco Romeo
TL;DR
This paper proves that certain classes of graphs, including wheels and block graphs, have sequentially Cohen-Macaulay binomial edge ideals, and introduces a method to construct new such graphs using cones.
Contribution
It establishes the sequentially Cohen-Macaulay property for wheels and block graphs and presents a new construction technique for generating more such graphs.
Findings
Wheels and block graphs have sequentially Cohen-Macaulay binomial edge ideals.
A construction method using cones produces new sequentially Cohen-Macaulay graphs.
Abstract
We prove that wheels and block graphs have sequentially Cohen-Macaulay binomial edge ideals. Moreover, we provide a construction of new families of sequentially Cohen-Macaulay graphs by cones.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Rings, Modules, and Algebras