On the Burkard-Hammer condition for hamiltonian split graphs |
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Authors: | Ngo Dac Tan |
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Affiliation: | a Institute of Mathematics, 18 Hoang Quoc Viet Road, 10307 Hanoi, Viet Nam b Provincial Office of Education and Training, Tuyen Quang, Viet Nam |
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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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Keywords: | primary 05C45 secondary 05C75 |
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