When a graph is drawn in a classical manner, its vertices are shown as small disks and its edges with a positive width; zero-width edges exist only in theory. Let r denote the rad...
We show that the modular decomposition of a countable graph can be defined from this graph, given with an enumeration of its set of vertices, by formulas of Monadic Second-Order l...
Abstract. Random graphs with given expected degrees G(w) were introduced by Chung and Lu so as to extend the theory of classical G(n, p) random graphs to include random power law g...
We consider the following vertex coloring problem. We are given an undirected graph G = (V, E), where each vertex v is associated with a penalty rejection cost rv. We need to choos...
Let H be a finite family of graphs. A graph G is H-universal if it contains a copy of each H H as a subgraph. Let H(k, n) denote the family of graphs on n vertices with maximum d...