We consider adding k shortcut edges (i.e. edges of small fixed length δ ≥ 0) to a graph so as to minimize the weighted average shortest path distance over all pairs of vertices...
Bounds on the minimum degree and on the number of vertices attaining it have been much studied for finite edge-/vertex-minimally kconnected/k-edge-connected graphs. We give an ove...
We study the following problem: Given a set V of n vertices and a set E of m edge pairs, we define a graph family G(V, E) as the set of graphs that have vertex set V and contain ...
A nonplanar graph G is near-planar if it contains an edge e such that G−e is planar. The problem of determining the crossing number of a near-planar graph is exhibited from diffe...