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Generalizing Sufficient Conditions and Traceable Graphs

  • Kewen Zhao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7389)

Abstract

In 2005, Rahman and Kaykobad proved that if G is a 2-connected graph with n vertices and d(u)+d(v)+((u,v)≥n+1 for each pair of distinct non-adjacent vertices u,v in G, then G is traceable [ Information Processing Letters, 94(2005), 1, 37-41]. In 2006, Li proved thatif G is a 2-connected graph with n vertices and d(u)+d(v)+((u,v)≥n+3 for each pair of distinct non-adjacent vertices u,v in G, then G is Hamiltonian-connected [Information Processing Letters, 98(2006), 4, 159-161]. In this present paper, we prove that if G is a 2-connected graph with n vertices and d(u)+d(v)+((u,v)≥n for each pair of distinct non-adjacent vertices u,v in G, then G has a Hamiltonian path or G belongs to a class of exceptional graphs. We also prove that if G is a 2-connected graph with n vertices and d(u)+d(v)+((u,v)≥n+2 for each pair of distinct non-adjacent vertices u,v in G, then G is Hamiltonian-connected or G belongs to a classes of exceptional graphs. Thus, our the two results generalize the above two results by Rahman et al. and Li, respectively.

Keywords

rahman-kaykobad condition new sufficient condition traceable graphs hamiltonian graphs Hamiltonian-connected 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Kewen Zhao
    • 1
  1. 1.Institute of Information Science and MathematicsQiongzhou UniversitySanyaP.R. China

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