Let G(V, E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product I1 × I2 × · · · × Ib, where ea...
A conjecture by D. Seese states that if a set of graphs has a decidable monadic second-order theory, then it is the image of a set of trees under a transformation defined by monad...
Let n(G) denote the number of vertices of a graph G and let (G) be the independence number of G, the maximum number of pairwise nonadjacent vertices of G. The Hall ratio of a grap...
We study several cost coloring problems, where we are given a graph and a cost function on the independent sets and are to find a coloring that minimizes the function costs of the...
Abstract. Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, t...