Vertex pursuit games, such as the game of Cops and Robbers, are a simplified model for network security. In these games, cops try to capture a robber loose on the vertices of the ...
In the recently introduced model for cleaning a graph with brushes, we use a degree-greedy algorithm to clean a random d-regular graph on n vertices (with dn even). We then use a d...
Margaret-Ellen Messinger, Pawel Pralat, Richard J....
Having in mind the large-scale analysis of gene regulatory networks, we review a graph decimation algorithm, called "leaf-removal", which can be used to evaluate the feed...
We show that nodes of high degree tend to occur infrequently in random graphs but frequently in a wide variety of graphs associated with real world search problems. We then study ...
In this paper we consider the classical Erd˝os-R´enyi model of random graphs Gn,p. We show that for p = p(n) ≤ n−3/4−δ , for any fixed δ > 0, the chromatic number χ...