Constructions for nonhamiltonian Burkard-Hammer graphs

Abstract

A graph G = (V,E) is called a split graph if there exists a partition V = I ∪ K such that the subgraphs G[I] and G[K] of G induced by I and K are empty and complete graphs, respectively. In 1980, Burkard and Hammer gave a necessary condition for split graphs with |I| < |K| to be hamiltonian. This condition is not sufficient. In this paper, we give two constructions for producing infinite families of split graphs with |I| < |K|, which satisfy the Burkard-Hammer condition but have no Hamilton cycles. © Springer-Verlag Berlin Heidelberg 2005.