Topology control is the problem of assigning transmission power values to the nodes of an ad hoc network so that the induced graph satisfies some specified property. The most fun...
The crossing number cr(G) of a graph G is the minimum number of crossings over all drawings of G in the plane. In 1993, Richter and Thomassen [RT93] conjectured that there is a co...
In this paper we prove that for any simple polygon P with n vertices, the sum of the number of strictly internal edges and the number of strictly external visibility edges of P is...
Let the trunk of a graph G be the graph obtained by removing all leaves of G. We prove that, for every integer c 2, there are at most finitely many trunks of semiharmonic graphs ...
Clustering methods usually require to know the best number of clusters, or another parameter, e.g. a threshold, which is not ever easy to provide. This paper proposes a new graph-b...