2 problems

Let $G$ be a graph and let $I_G$ be its cut ideal. A graph is $K_5$-minor-free when it has no minor isomorphic to $K_5$. Quartic generation conjecture. … This extends the proposed…

Let $G$ be a graph, let $I_G$ be its cut ideal, and let $\mu(I_G)$ denote the maximal degree of a binomial in a minimal generating set of $I_G$. A graph $H$ is a minor of $G$ if it…