We study a random graph Gn that combines certain aspects of geometric random graphs and preferential attachment graphs. The vertices of Gn are n sequentially generated points x1, ...
We describe the rst parallel algorithm with optimal speedup for constructing minimum-width tree decompositions of graphs of bounded treewidth. On n-vertex input graphs, the algori...
For a directed graph G without loops or parallel edges, let (G) denote the size of the smallest feedback arc set, i.e., the smallest subset X E(G) such that G \ X has no directed...
We consider the performance of a simple greedy matching algorithm MINGREEDY when applied to random cubic graphs. We show that if λn is the expected number of vertices not matched...
We prove that there is an absolute constant C > 0 so that for every natural n there exists a trianglefree regular graph with no independent set of size at least C n log n.