Biclique-maximizing conjecture for antiferromagnetic models

Prove that every antiferromagnetic model is biclique-maximizing; equivalently, establish that for every graph without isolated vertices and every antiferromagnetic model H, the inequality hom(G,H) ≤ ∏_{uv∈E(G)} hom(K_{d_u,d_v},H)^{1/(d_ud_v)} holds.

Background

The paper establishes the lower-bound side of an extremal picture for antiferromagnetic models: complete graphs minimize normalized weighted homomorphism counts. The complementary expected upper bound is formulated through bicliques, which maximize the corresponding normalized quantity for several classes of models and graphs.

The cited conjecture asserts that this biclique-maximizing inequality should hold for every antiferromagnetic model. Unlike the clique-minimization conjectures resolved by the paper, this conjecture is explicitly identified as still unresolved.