Let G = (V, E) be a graph. Let c : V → N be a vertex-coloring of the vertices of G. For any vertex u, we denote by N[u] its closed neighborhood (u and its adjacent vertices), an...
Inspired by a question of Lov´asz, we introduce a hierarchy of nested semidefinite relaxations of the convex hull of real solutions to an arbitrary polynomial ideal, called theta...
In this paper, we give a sufficient condition for a graph to have a degree bounded spanning tree. Let n ≥ 1, k ≥ 3, c ≥ 0 and G be an n-connected graph. Suppose that for eve...
Given a connected graph G and a failure probability pe for each edge e in G, the reliability of G is the probability that G remains connected when each edge e is removed independe...
We study communication in known topology radio networks with the presence of interference constraints. We consider a real-world situation, when a transmission of a node produces an...