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.
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