Let G be a connected plane geometric graph with n vertices. In this paper, we study bounds on the number of edges required to be added to G to obtain 2-vertex or 2-edge connected ...
: A well-known result of Tutte states that a 3-connected graph G is planar if and only if every edge of G is contained in exactly two induced non-separating circuits. Bixby and Cun...
The 2-Disjoint Connected Subgraphs problem asks if a given graph has two vertex-disjoint connected subgraphs containing prespecified sets of vertices. We show that this problem is...
Dynamic graph connectivity algorithms have been studied for many years, but typically in the most general possible setting, where the graph can evolve in completely arbitrary ways...
— We take a structural approach to the problem of designing the edge weights in an undirected graph subject to an upper bound on their total, so as to maximize the algebraic conn...
Yan Wan, Sandip Roy, Xu Wang, Ali Saberi, Tao Yang...