4 problems

Let $G$ range over $\Delta$-regular graphs, let $\alpha_G(B,\lambda)$ be the occupancy fraction, and let $F_G(B,\lambda)$ be the free energy density. Bipartite maximizer and clique…

For each $k\geqslant 1$, let $N_k$ be an integer, and let $G$ be a minimal $k$-extendable bipartite graph of order $n$ and size $|E|$. Eventual size bound conjecture. There exists…

Let $G$ be a minimal $k$-extendable bipartite graph, where $k\geqslant 1$, and let $n$ be its order. Let $V_{k+1}$ be the set of vertices of degree precisely $k+1$. Order bound con…

Let $G$ be a minimal $k$-extendable bipartite graph, with $k\geqslant 1$, order $n$, and size $m=|E(G)|$. Let $V_{k+1}$ be the set of vertices of degree precisely $k+1$. Main conje…