Necessary conditions for Hamiltonian split graphs (Q1057287)

The problem investigated in this paper is if a necessary condition for Hamiltonian split graphs developed by \textit{R. Burkard} and \textit{P. L. Hammer} [J. Comb. Theory, Ser. B 28, 245-248 (1980; Zbl 0403.05058)] can be sharpened to a necessary and sufficient one. First, a simplified version of the Burkard and Hammer-condition is given. Then, considering missing edges instead of missing vertices a new necessary condition is proved. From this, the Burkard and Hammer-condition and other new conditions can be derived as a corollary. Nevertheless, it is possible to prove all these conditions to be equivalent to each other.