On \(m\)-closed graphs
Summary: A graph is closed when its vertices have a labeling by \([n]\) such~that the binomial edge ideal \(J_G\) has a quadratic Gröbner~basis~with respect to the lexicographic order induced by \(x_1> \ldots> x_n > y_1> \ldots > y_n\). In this paper, we generalize this notion~and study the so called \(m\)-closed graphs. We find equivalent condition to \(3\)-closed property of an arbitrary tree \(T\). Using it, we classify a class of \(3\)-closed trees. The primary~decomposition of this class of graphs is also studied.
scientific article; zbMATH DE number 6369272
scientific article