Abstract
The main result of the paper is the following
Theorem. Let D=(X,Y,A) be a bipartite, balanced digraph of order 2n and size at least 2n2−2n+3. Then D contains an almost symmetric Hamiltonian cycle (i.e. a Hamiltonian cycle in which at least 2n−1 arcs are symmetric edges), unless D has a vertex which is not incident to any symmetric edge of D.
This theorem implies a number of results on cycles in bipartite, balanced digraphs, including some recent results of N. Chakroun, M. Manoussakis and Y. Manoussakis.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. Berge,Graphes et Hypergraphes, Dunod 1973.
J. C. Bermond andC. Thomassen, Cycles in digraphis—A survey,J. Graph Theory 5 (1981), 1–43.
N. Chakroun, M. Manoussakis andY. Manoussakis, accepted for publication in:Combinatorics and Graph Theory, Banach Center Publications, editors: M. Borowiecki and Z. Skupien, Vol. 35.
M. Manoussakis andY. Manoussakis, Number of arcs, cycles and paths in bipartite digraphs,preprint.
J. Mitchen andE. Schmeichel, Pancyclic and bipancyclic graphs—A survey,Colorado Symposium on Graph Theory.
J. W. Moon andL. Moser, On Hamiltonian bipartite graphs,Israel. J. Math. 1 (1963), 163–165.
A. P. Wojda, Orientations of Hamiltonian cycles in large digraphs,J. Graph Theory 10 (1986), 211–218.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wojda, A.P., Woźniak, M. Orientations of Hamiltonian cycles in bipartite digraphs. Period Math Hung 28, 103–108 (1994). https://doi.org/10.1007/BF01876900
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01876900