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Transactions ID Number: 52-354
Full Name: kewen zzhao
Position: Professor
Age: ON
Sex: Male
Address: qiongzhou university, Sanya,Hainan
Country: CHINA
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E-mail address: kwzqzu@yahoo.cn
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Title of the Paper: Neighborhood conditions and Hamiltonian-connected graphs
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Number of paper pages: 10
Abstract: A graph G with at least three vertices is said to be Hamiltonian-connected if each pair distinct vertices is connected by a Hamiltonian path. If uv is a edge of Hamiltonian-connected graph G, then there must exist a Hamiltonian cycle containing uv. If C1,C2,¡Cr are distinct Hamiltonian cycles, and if edge xyE(C1¡ÈC2¡È¡Cr), then we can obtain Hamiltonian cycle Cr+1 containing xy and clearly Cr+1 is different from C1,C2,¡Cr. Thus, a Hamiltonian-connected graph has very many Hamiltonian cycles, so we can see the sufficient conditions of Hamiltonian-connected is stronger than Hamiltonian and pancyclic. Therefore, we always can see that many great improvements of bounds of conditions for Hamiltonian have already been done, but this is somewhat difficult for Hamiltonian-connected yet. In 1989 Faudree et al. considerd 3-connected graphs and proved that if G is a 3-connected graph of order n and NC¡Ý2n/3, then G is Hamiltonian-connected graph. In this paper we i!
nvestigate further 2-connected graphs with better bound (2n-1)/3 and prove that if G is a 2-connected graph of order n and NC¡Ý(2n-1)/3, then G is Hamiltonian-connected graph or G§¨
Keywords: Hamiltonian-connected graphs; Hamiltonian graphs; Hamiltonian paths; Hamiltonian cycles; Neighborhood unions; Paths.
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