×

An infinite family of planar non-Hamiltonian bihomogeneously traceable oriented graphs. (English) Zbl 1231.05163

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

MSC:

05C45 Eulerian and Hamiltonian graphs
05C20 Directed graphs (digraphs), tournaments
05C10 Planar graphs; geometric and topological aspects of graph theory
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Bermond J.-C., Simões-Pereira J.M.S., Zamfirescu C.M.: On hamiltonian homogeneously traceable digraphs. Math. Jpn. 24, 423–426 (1979) · Zbl 0422.05030
[2] Fouquet J.-L., Jolivet J.-L.: Hypohamiltonian oriented graphs. Cahiers Centre Études Rech. Opér 20, 171–181 (1978) · Zbl 0381.05039
[3] Grötschel M., Wakabayashi Y.: Hypohamiltonian digraphs. J. Methods Oper. Res. 36, 99–119 (1980) · Zbl 0436.05038
[4] Hahn S., Zamfirescu T.: Bihomogeneously traceable oriented graphs. Rend. Sem. Mat. Univ. Politec. Torino 39(2), 137–145 (1981) · Zbl 0518.05036
[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)
[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) · Zbl 0763.05068
[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) · Zbl 0371.05015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.