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 ...

The Erdős–Pósa property forms a pivotal concept in modern graph theory by establishing a profound duality between the problems of packing and covering cycles or other substructures. At its core, this ...

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 ...

KALAMAZOO, Mich.—Western Michigan University's international reputation on the topic of graph theory is on display in a new book published recently by Princeton University Press. Graph theory, a ...

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 ...

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 ...