On k-Transitive Closures of Directed Paths

Krzysztof Pszczoła^*

Institute of Mathematics, Jan Kochanowski University, Kielce, Poland.

DOI: 10.4236/apm.2015.512066                

Abstract

In this paper we study the structure of k-transitive closures of directed paths and formulate several properties. Concept of k-transitive orientation generalizes the traditional concept of transitive orientation of a graph.

Keywords

Digraph, Transitive Graph, k-Transitive Digraph, k-Transitive Closure of an Oriented Graph

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Kelly, D. (1985) Comparability Graphs. In: Rival, I., Ed., Graphs and Order. The Role of Graphs in the Theory of Ordered Sets and Its Applications, North Holland, Dordrecht, 3-40. http://dx.doi.org/10.1007/978-94-009-5315-4_1
[2]	Gyárfás, A., Jacobson, M.S. and Kinch, L.F. (1988) On a Generalization of Transitivity for Digraphs. Discrete Mathematics, 69, 35-41. http://dx.doi.org/10.1016/0012-365X(88)90175-6
[3]	Tuza, Z. (1994) Characterization of (m,1)-Transitive and (3,2)-Transitive Semi-Complete Directed Graphs. Discrete Mathematics, 135, 335-347. http://dx.doi.org/10.1016/0012-365X(94)00060-V
[4]	Hernández-Cruz, C. (2012) 3-Transitive Digraphs. Discussiones Mathematicae Graph Theory, 32, 205-219. http://dx.doi.org/10.7151/dmgt.1613
[5]	Hernández-Cruz, C. and Montellano-Ballesteros, J.J. (2014) Some Remarks on the Structure of Strong k-Transitive Digraphs. Discussiones Mathematicae Graph Theory, 34, 651-671. http://dx.doi.org/10.7151/dmgt.1765