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Degree sums,k-factors and hamilton cycles in graphs

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Abstract

We prove (a generalization of) the following conjecture of R. Häggkvist: LetG be a 2-connected graph onn vertices where every pair of nonadjacent vertices has degree sum at leastn — k and assume thatG has ak-factor; thenG is hamiltonian. This result is a common generalization of well-known theorems of Ore and Jackson, respectively.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Memphis State University, 38152, Memphis, TN, USA

    R. J. Faudree

  2. Faculty of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    J. van den Heuvel

Authors
  1. R. J. Faudree
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  2. J. van den Heuvel
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Additional information

The research for this paper was done while the second author visited Memphis State University, partly supported by a grant from the Netherlands Organization for Scientific Research (N.W.O.).

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Faudree, R.J., van den Heuvel, J. Degree sums,k-factors and hamilton cycles in graphs. Graphs and Combinatorics 11, 21–28 (1995). https://doi.org/10.1007/BF01787418

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  • DOI: https://doi.org/10.1007/BF01787418

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