In a previous paper we showed that a random 4-regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. Here we extend the method to show that a random 6-regular...
In 1972, M. Rosenfeld asked if every triangle-free graph could be embedded in the unit sphere Sd in such a way that two vertices joined by an edge have distance more than √ 3 (i...
Let G be a connected graph, and let V and V two n-element subsets of its vertex set V (G). Imagine that we place a chip at each element of V and we want to move them into the posi...
A set of vertices C in a graph is convex if it contains all vertices which lie on shortest paths between vertices in C. The convex hull of a set of vertices S is the smallest conve...
Motivated by questions in computer vision and sensor networks, Alpert et al. [3] introduced the following definitions. Given a graph G, an obstacle representation of G is a set of...