Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...

One of the highlights in the Robertson-Seymour theory on graph minors is the finiteness (for each fixed surface S) of the set of the minimal forbidden minors for S. Theorem 7.0.1 (Robertson and ...

We consider ferromagnetic Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We ...

Recently, Knuth and Ciucu independently proved the surprising fact, conjectured by Stanley, that one connected component of the tensor product of a path with itself (the so-called "Aztec diamond graph ...