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On the Hamiltonian-Connectedness for Graphs Satisfying Ore’s Theorem

  • Yuan-Kang Shih
  • Hsun Su
  • Shin-Shin Kao
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 20)

Abstract

Consider any undirected and simple graph G = (V,E), where V and E denote the vertex set and the edge set of G, respectively. Let |G| = |V| = n ≥ 3. The well-known Ore’s theorem states that if deg G (u) + deg G (v) ≥ n holds for each pair of nonadjacent vertices u and v of G, then G is hamiltonian. A similar theorem given by Erdös is as follows: if deg G (u) + deg G (v) ≥ n + 1 holds for each pair of nonadjacent vertices u and v of G, then G is hamiltonian-connected. In this paper, we improve both theorems by showing that any graph G satisfying the condition in Ore’s theorem is hamiltonian-connected unless G belongs to two exceptional families.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Yuan-Kang Shih
    • 1
  • Hsun Su
    • 2
  • Shin-Shin Kao
    • 3
  1. 1.Intel-NTU Connected Context Computing CenterNational Taiwan UniversityTaipeiTaiwan, R.O.C.
  2. 2.Department of Public Finance and TaxationTakming University of Science and TechnologyTaipei CityTaiwan, R.O.C.
  3. 3.Department of Applied MathematicsChung Yuan Christian UniversityChung-Li CityTaiwan, R.O.C.

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