Weakly closed graphs and F-purity of binomial edge ideals · arXivDesk
1209.4300Sep 19, 201212 pages, Major Revision(The organization of this paper has changed: Section1: Definition of the weakly closed graph and discussion about between the closed graph and the weakly closed graph, Section2: $F$-purity of binomial edge ideals associated with weakly closed graphs, Section3: Classification of all connected weakly closed graphs with 5 and 6 vertex. ) , References added
Weakly closed graphs and F-purity of binomial edge ideals
Herzog-Hibi-Hreindóttir-Kahle-Rauh introduced the class of closed graph and they proved that the binomial edge ideal J(G) of a graph G has quadratic Gröbner bases if G is closed. In this paper, we introduce the class of weakly closed graph as a generalization of the closed graph and prove that the quotient ring S/J(G) is F
Nearby in the stack
-pure if
G
is weakly closed. This fact is a generalization of Ohtani's theorem.