In a recent paper, Amini et al. introduced a general framework to prove duality theorems between tree decompositions and their dual combinatorial object. They unify all known ad-h...
Abstract. The study of graph vertex colorability from an algebraic perspective has introduced novel techniques and algorithms into the field. For instance, it is known that k-color...
We study a local version of the order property in several frameworks, with an emphasis on frameworks where the compactness theorem fails: (1) Inside a fixed model, (2) for classes ...
A subgraph H of a graph G is gated if for every x V(G) there exists a vertex u in H such that dG (x, v) = dG (x, u) + d G (u, v) for any v V(H). The gated amalgam of graphs G 1 an...
We explore the intricate interdependent relationship among counting problems, considered from three frameworks for such problems: Holant Problems, counting CSP and weighted H-color...