This is a preview. Log in through your library . Abstract This paper considers the planar decomposition of a complete bipartite graph, that is, the decomposition of a complete bipartite graph into ...

In an interesting recent article [4], J. W. Moon has given a list of properties of the graph L(Bmn) (to be defined more precisely below) and investigated the question of whether these properties ...

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 ...

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. It is ...