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Bounds on the minimum degree and on the number of vertices attaining it have been much studied for finite edge-/vertex-minimally kconnected/k-edge-connected graphs. We give an ove...
We consider the problem of finding obnoxious centers in graphs. For arbitrary graphs with n vertices and m edges, we give a randomized algorithm with O(n log2 n + m log n) expecte...
The firefighter problem is the following discrete-time game on a graph. Initially, a fire starts at a vertex of the graph. In each round, a firefighter protects one vertex not yet ...
In this paper we consider the problem of computing the expected hitting time to a vertex for random walks on graphs. We give a method for computing an upper bound on the expected ...
Let (Cd m) denote the graph whose set of vertices is Zd m in which two distinct vertices are adjacent iff in each coordinate either they are equal or they differ, modulo m, by at