Abstract We study homological properties of random quadratic monomial ideals in a polynomial ring $R = {\mathbb {K}}[x_1, \dots x_n]$, utilizing methods from the Erd̋s–Rényi model graphs. Here, for graph $G \sim G(n, p),$ we consider coedge ideal $I_G$ generated by monomials corresponding to missing edges $G$ and Betti numbers $R/I_G$ as $n$ tends infinity. Our main results involve setting edge ...

We construct the first linear strand of minimal free resolutions edge ideals d-partite d-uniform clutters. show that such are supported on relative simplicial complexes. In case clutters have resolutions, we give an explicit and surprisingly simple description their generalizing known for Ferrers graphs hypergraphs co-letterplace ideals. As application, Lyubeznik numbers appear last column tabl...

Finite obstruction set characterizations for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. In this paper we characterize several families of graphs with small feedback sets, namely k1-Feedback Vertex Set, k2-Feedback Edge Set and (k1,k2){Feedback Vertex/Edge Set, for small integer parameters k1 and k2. Our constructive methods can compute obstruction sets f...