Acta Mathematica Vietnamica

Print

 

Squarefree Monomial Ideals that Fail the Persistence Property and Non-increasing Depth
Huy Tài Hà, Mengyao Sun

 

Abstract

In a recent work (Kaiser et al., J. Comb. Theory Ser. A 123, 239–251, 2014), Kaiser et al. provide a family of critically 3-chromatic graphs whose expansions do not result in critically 4-chromatic graphs and, thus, give counterexamples to a conjecture of Francisco et al. (Discrete Math. 310, 2176–2182, 2010). The cover ideal of the smallest member of this family also gives a counterexample to the persistence and non-increasing depth properties. In this paper, we show that the cover ideals of all members of their family of graphs indeed fail to have the persistence and non-increasing depth properties.

You are here: Home No. 1