We present an algorithm that allows swarms of robots to navigate in environments containing unknown obstacles, moving towards and spreading along 2D shapes given by implicit funct...
Abstract. Path deformation is a technique that was introduced to generate robot motion wherein a path, that has been computed beforehand, is continuously deformed on-line in respon...
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 ...