Advertisement

Graphs and Combinatorics

, Volume 26, Issue 1, pp 141–146 | Cite as

An Infinite Family of Planar Non-Hamiltonian Bihomogeneously Traceable Oriented Graphs

Original Paper

Abstract

We answer an open question on planar non-hamiltonian bihomogeneously traceable digraphs without opposite arcs by constructing an infinite family of such graphs.

Keywords

Planar Bihomogeneously traceable Digraph 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bermond J.-C., Simões-Pereira J.M.S., Zamfirescu C.M.: On hamiltonian homogeneously traceable digraphs. Math. Jpn. 24, 423–426 (1979)MATHGoogle Scholar
  2. 2.
    Fouquet J.-L., Jolivet J.-L.: Hypohamiltonian oriented graphs. Cahiers Centre Études Rech. Opér 20, 171–181 (1978)MATHMathSciNetGoogle Scholar
  3. 3.
    Grötschel M., Wakabayashi Y.: Hypohamiltonian digraphs. J. Methods Oper. Res. 36, 99–119 (1980)MATHGoogle Scholar
  4. 4.
    Hahn S., Zamfirescu T.: Bihomogeneously traceable oriented graphs. Rend. Sem. Mat. Univ. Politec. Torino 39(2), 137–145 (1981)MATHMathSciNetGoogle Scholar
  5. 5.
    Skupień, Z.: On homogeneously traceable nonhamiltonian digraphs and oriented graphs. In: Proc. Fourth Int. Conf. on the Theory and Appl. of Graphs, Kalamazoo (MI) 1980, pp. 517–527. Wiley, New York (1981)Google Scholar
  6. 6.
    Skupień, Z.: Exponential constructions of some nonhamiltonian minima. In: Proc. Fourth CS Symposium on Combinatorics, Graphs and Complexity, Prachatice 1990, Ann. Discrete Math., vol. 51, pp. 321–328 (1992)Google Scholar
  7. 7.
    Thomassen, C.: Hypohamiltonian graphs and digraphs. In: Proc. Int. Conf. on the Theory and Appl. of Graphs, Kalamazoo (MI) 1976, Lect. Notes Math., vol. 642, pp. 557–571. Springer, Berlin (1978)Google Scholar

Copyright information

© Springer 2010

Authors and Affiliations

  1. 1.Fakultät für MathematikTechnische Universität DortmundDortmundGermany

Personalised recommendations