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Vietnam Journal of Mathematics 37:2&3 (2009) 379-386 

On the Hamiltonian and Classification Problems for some Families of Split Graphs

Ngo Dac Tan

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 this paper, we survey results on the hamiltonian and classification problems for split graphs G with the minimum degree δ(G)≥ |I|-4.

2000 Mathematics Subject Classification: 05C45, 05C75.

Keywords: Split graph, Burkard-Hammer condition, Burkard-Hammer graph, hamiltonian graph, maximal nonhamiltonian split graph.

Vietnam Academy of Science and Technology & Vietnamese Mathematical Society
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