A. J. Hoffman, On the Line Graph of the Complete Bipartite Graph, The Annals of Mathematical Statistics, Vol. 35, No. 2 (Jun., 1964), pp. 883-885 ...

Barnette's Conjecture: Every 3-connected cubic planar bipartite graph is Hamiltonian. It is known that this is not true if you remove the "bipartite" condition, but the smallest 3-connected cubic ...

The shadow graph S (G) of a graph G is that graph obtained from G by adding to G a new vertex z′ for each vertex z of G and joining z′ to the neighbors of z in G. All those graphs G for which S (G) is ...

Let us say that a graph is k- apex if it contains a set of at most k vertices whose removal yields a planar graph. We define the apex number of a graph G as the minimum k for which G is k-apex.