2405.08671May 14, 2024In this new version, we added Example 1.6 to show that proving sequentially Cohen-Macaulayness by the vanishing of local cohomology modules, also for trees, is a hard task. We generalized Proposition 1.8 for any homogeneous ideal in Lemma 1.9. Last, we modified the head of Section 2, by citing Zafar's results of his study on the approximately Cohen-Macaulayness of binomial edge ideals of cycles
Sequentially Cohen-Macaulay binomial edge ideals
Ernesto Lax, Giancarlo Rinaldo, Francesco Romeo
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.