IJPAM: Volume 32, No. 4 (2006)

NEIGHBORHOOD CONDITIONS AND
HAMILTONIAN PATHS IN GRAPHS

Kewen Zhao
Department of Mathematics
University of Qiongzhou
Wuzhishan, Hainan, 572200, P.R. CHINA
e-mail: kewen@bxemail.com


Abstract.Let NC=min{ $ \vert $ N(u) $ \cup $ N(v) $ \vert $:u,v $ \in
$ V(G),uv $ \notin $ E(G)}. In 1989 Faudree et al obtained that if G is a 3-connected graph of order n with NC $ \ge $ (2n+1)/3, then G is Hamilton-connected graph. In this paper we prove the further result that if G is a 3-connected graph of order n with NC $ \ge $ 2n/3, then G is Hamilton-connected graph.

Received: December 12, 2005

AMS Subject Classification: 05C38, 05C45

Key Words and Phrases: Hamilton-connected graphs, neighborhood unions, paths

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 32
Issue: 4