Consider the edge-connectivity survivable network design problem: given a graph G = (V, E) with edge-costs, and edgeconnectivity requirements rij Z0 for every pair of vertices i,...
We show that for every connected graph G of diameter 3, the graph G3 has average degree 7 4 (G). We also provide an example showing that this bound is best possible. This resolv...
Let k denote the maximum degree of the kth iterated line graph Lk(G). For any connected graph G that is not a path, the inequality k+1 2k - 2 holds. Niepel, Knor, and Solt
Given a simple graph G, the graph associahedron KG is a simple polytope whose face poset is based on the connected subgraphs of G. This paper defines and constructs graph associah...