While it is exponentially unlikely that a sparse random graph or hypergraph is connected, with probability 1 − o(1) such a graph has a “giant component” that, given its numbe...
Relational graphs are widely used in modeling large scale networks such as biological networks and social networks. In this kind of graph, connectivity becomes critical in identif...
Abstract. We study the Edge Disjoint Paths (EDP) problem in undirected graphs: Given a graph G with n nodes and a set T of pairs of terminals, connect as many terminal pairs as pos...
For several graph-theoretic parameters such as vertex cover and dominating set, it is known that if their sizes are bounded by k then the treewidth of the graph is bounded by some ...
Erik D. Demaine, Fedor V. Fomin, Mohammad Taghi Ha...
Recurrence relations are derived for the numbers of labeled 3-regular graphs with given connectivity, order, number of double edges, and number of loops. This work builds on metho...
Gab-Byung Chae, Edgar M. Palmer, Robert W. Robinso...