3 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…

Let $\alpha_G(\lambda)$ denote the occupancy fraction of a graph $G$ in the hard-core model, and let $H_{4,6}$ be the $(4,6)$-cage. (4,6)-cage occupancy-fraction conjecture. For ev…

Let $\alpha_G(\lambda)$ denote the occupancy fraction of a graph $G$ in the hard-core model, and let $H_{3,8}$ be the $(3,8)$-cage, also known as the Levi graph or Tutte–Coxeter gr…