DMGT

Discussiones Mathematicae Graph Theory 28(1) (2008) 23-34
DOI: https://doi.org/10.7151/dmgt.1389

COMPETITION HYPERGRAPHS OF DIGRAPHS WITH CERTAIN PROPERTIES II HAMILTONICITY

Martin Sonntag

Faculty of Mathematics and Computer Science
TU Bergakademie Freiberg
Prüferstraße 1, D-09596 Freiberg, Germany
e-mail: sonntag@mathe.tu-freiberg.de

Hanns-Martin Teichert

Institute of Mathematics
University of Lübeck
Wallstraß e 40, D-23560 Lübeck, Germany
e-mail: teichert@math.uni-luebeck.de

Abstract

If D = (V,A) is a digraph, its competition hypergraph C H(D) has vertex set V and e ⊆ V is an edge of C H(D) iff |e| ≥ 2 and there is a vertex v ∈ V, such that e = N_D⁻(v) = {w ∈ V|(w,v) ∈ A}. We give characterizations of C H(D) in case of hamiltonian digraphs D and, more general, of digraphs D having a τ-cycle factor. The results are closely related to the corresponding investigations for competition graphs in Fraughnaugh et al. [4] and Guichard [6].

Keywords: hypergraph, competition graph, hamiltonian digraph.

2000 Mathematics Subject Classification: 05C65, 05C20, 05C45.

References

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Received 14 January 2005
Revised 24 September 2007
Accepted 31 December 2007