We prove that the threshold for a random graph to have a k-core is equal to the threshold for having a subgraph which meets a necessary condition of Gallai for being k-critical. 1...
This paper presents algorithms to find vertex-critical and edgecritical subgraphs in a given graph G, and demonstrates how these critical subgraphs can be used to determine the ch...
Christian Desrosiers, Philippe Galinier, Alain Her...
We propose a new exact algorithm for finding the chromatic number of a graph G. The algorithm attempts to determine the smallest possible induced subgraph G' of G which has t...
We consider a random subgraph Gp of a host graph G formed by retaining each edge of G with probability p. We address the question of determining the critical value p (as a function...