Graph H is a root of graph G if there exists a positive integer k such that x and y are adjacent in G if and only if their distance in H is at most k. Motwani and Sudan [1994] prov...
Abstract. A trivalent diagram is a connected, two-colored bipartite graph (parallel edges allowed but not loops) such that every black vertex is of degree 1 or 3 and every white ve...
Abstract. We show that finding roots of Boolean matrices is an NPhard problem. This answers a twenty year old question from semigroup theory. Interpreting Boolean matrices as dire...
A plane graph is a drawing of a planar graph in the plane such that no two edges cross each other. A rooted plane graph has a designated outer vertex. For given positive integers ...
This paper presents new graph-theoretic results appropriate to the analysis of a variety of consensus problems cast in dynamically changing environments. The concepts of rooted, s...