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Necessary conditions for Hamiltonian split graphs. (English) Zbl 0563.05041

The problem investigated in this paper is if a necessary condition for Hamiltonian split graphs developed by R. Burkard and 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.

MSC:

05C45 Eulerian and Hamiltonian graphs

Citations:

Zbl 0403.05058
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