Cycle lengths in polytopal graphs

  • Joseph Malkevitch
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 642)


If G is a hamiltonian 3-polytopal graph with n vertices, G will be called almost pancyclic of order m (m ≥ 3, m < n) if G has cycles of all lengths other than m. Some constructions are given for 3-valent 3-polytopal graphs which are almost pancyclic of order m, and some related results and problems are discussed.


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  1. 1.
    J. A. Bondy, Cycles in graphs. Combinatorial Structures and Their Applications. Gordon and Breach, New York (1970) 15–18.Google Scholar
  2. 2.
    J. A. Bondy, Pancyclic Graphs I, J. Combinatorial Theory 11 (1971) 80–84.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    B. Grünbaum, Convex Polytopes. Interscience-Wiley, London, New York, Sydney (1967).zbMATHGoogle Scholar
  4. 4.
    V. Jacos and S. Jendrol, A problem concerning j-pancyclic graphs. Matematicky Casopis. 24 (1974) 259–262.MathSciNetzbMATHGoogle Scholar
  5. 5.
    L. Lovász and M. D. Plummer, On a family of planar bicritical graphs. Proc. London Math. Soc. (3) 30 (1975) 187–208.Google Scholar
  6. 6.
    J. Malkevitch, On the lengths of cycles in planar graphs. Recent Trends in Graph Theory. Springer-Verlag. Berlin, Heidelberg and New York (1970) 191–195.Google Scholar
  7. 7.
    G. H. J. Meredith, Cyclic and Colouring Properties of Graphs PhD Thesis. Southampton University (1973).Google Scholar
  8. 8.
    E. F. Schmeicher and S. L. Hakimi. Pancyclic graphs and a conjecture of Bondy and Chvatal. J. of Combinatorial Theory (B) 17 (1974) 22–34.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Joseph Malkevitch
    • 1
  1. 1.York College (C.U.N.Y.)JamaicaUSA

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