Degree conditions for k-ordered hamiltonian graphs

  • Authors:

  • Ralph J. Faudree;Ronald J. Gould;Alexandr V. Kostochka;Linda Lesniak;Ingo Schiermeyer;Akira Saito

  • Affiliations:

  • Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee 38152;Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322;Department of Mathematics, University of Illinois, at Urbana-Champaign, Urbana, IL 61801 and Institute of Mathematics, 630090 Novosibirsk, Russia;Department of Mathematics and Computer Science, Drew University, Madison, New Jersey 07940;Department of Mathematics and Computer Science, Freiberg University of Mining and Technology, D-09596 Freiberg, Germany;Department of Applied Mathematics, Nihon University, Tokyo 156, Japan

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2003

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Abstract

For a positive integer k, a graph G is k-ordered hamiltonian if for every ordered sequence of k vertices there is a hamiltonian cycle that encounters the vertices of the sequence in the given order. It is shown that if G is a graph of order n with 3 ≤ k ≤ n-2, and deg(u) + deg(v) ≥ n + (3k - 9)-2 for every pair u, v of nonadjacent vertices of G, then G is k-ordered hamiltonian. Minimum degree conditions are also given for k-ordered hamiltonicity. © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 199–210, 2003