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 di...
Given a graph on n vertices which is the union of two comparability graphs on the same vertex set, it always contains a clique or independent set of size n 1 3 . On the other hand...
The edge clique graph of a graph G is one having as vertices the edges of G, two vertices being adjacent if the corresponding edges of G belong to a common clique. We describe cha...
We prove that a claw-free, 2-connected graph with fewer than 18 vertices is traceable, and we determine all non-traceable, claw-free, 2-connected graphs with exactly 18 vertices an...
Network visualisations use clustering approaches to simplify the presentation of complex graph structures. We present a novel application of clustering algorithms, which controls ...