ArticleOriginal scientific text
Title
A classification for maximal nonhamiltonian Burkard-Hammer graphs
Authors 1, 2
Affiliations
- Institute of Mathematics, 18 Hoang Quoc Viet Road, 10307 Hanoi, Vietnam
- Department of Mathematics, Mahasarakham University, Kamrieng, Kantarawichai, Mahasarakham 44150, Thailand
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 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.
Keywords
split graph, Burkard-Hammer condition, Burkard-Hammer graph, hamiltonian graph, maximal nonhamiltonian split graph
Bibliography
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Pages:
67-89
Main language of publication
English
Received
2006-09-22
Accepted
2007-05-21
Published
2008
DOI: 10.7151/dmgt.1392
Exact and natural sciences