2 problems

Let $G$ be an unmixed vertex decomposable graph, and let $J(G)$ be its vertex cover ideal. Weak graph conjecture. Then … This is presented as a weak form of the conjecture for pure…

Let $I=(x^a,y^b)\cap (y^c,z^d)\cap (x^e,z^f)$, where … Write $A(I)$ for the symbolic Rees algebra of $I$, and let $d(A(I))$ denote its depth. Lower-bound conjecture. … This propose…