Abstract
A graph G = ( V , E ) is called a split graph if there exists a partition V = I ∪ K such that the subgraphs of G induced by I and K are empty and complete graphs, respectively. In 1980, Burkard and Hammer gave a necessary but not sufficient condition for hamiltonian split graphs with | I | < | K | . In this paper, we show that the Burkard–Hammer condition is also sufficient for the existence of a Hamilton cycle in a split graph G such that 5 ≠ | I | < | K | and the minimum degree δ ( G ) ⩾ | I | - 3 . For the case 5 = | I | < | K | , all split graphs satisfying the Burkard–Hammer condition but having no Hamilton cycles are also described.
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