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A classification for maximal nonhamiltonian Burkard-Hammer graphs

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Tan N., Iamjaroen C.

Discussiones Mathematicae Graph Theory

2008

tom 28

nr 1

67-89

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 1980, Burkard and Hammer gave a necessary condition for a split graph G with |I| < |K| to be hamiltonian. We will call a split graph G with |I| < |K| satisfying this condition a Burkard-Hammer graph. Further, a split graph G is called a maximal nonhamiltonian split graph if G is nonhamiltonian but G+uv is hamiltonian for every uv ∉ E where u ∈ I and v ∈ K. Recently, Ngo Dac Tan and Le Xuan Hung have classified maximal nonhamiltonian Burkard-Hammer graphs G with minimum degree δ(G) ≥ |I|- 3. In this paper, we classify maximal nonhamiltonian Burkard-Hammer graphs G with |I| ≠ 6,7 and δ(G) = |I| - 4.

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1 Discussiones Mathematicae Graph Theory

1 Iamjaroen C.

1 Tan N.

1 2008

Wyniki wyszukiwania

A classification for maximal nonhamiltonian Burkard-Hammer graphs