DMGT

Discussiones Mathematicae Graph Theory 28(1) (2008) 5-21
DOI: https://doi.org/10.7151/dmgt.1388

COMPETITION HYPERGRAPHS OF DIGRAPHS WITH CERTAIN PROPERTIES I STRONG CONNECTEDNESS

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 CH(D) has the vertex set V and e ⊆ V is an edge of CH(D) iff |e| ≥ 2 and there is a vertex v ∈ V, such that e = {w ∈ V|(w,v) ∈ A}. We tackle the problem to minimize the number of strong components in D without changing the competition hypergraph CH(D). The results are closely related to the corresponding investigations for competition graphs in Fraughnaugh et al. [3].

Keywords: hypergraph, competition graph, strong component.

2000 Mathematics Subject Classification: 05C65, 05C20, 05C40.

References

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[4]	S.R. Kim, The competition number and its variants, in: J. Gimbel, J.W. Kennedy and L.V. Quintas (eds.), Quo vadis, graph theory?, Ann. of Discrete Math. 55 (1993) 313-326.
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[7]	F.S. Roberts amd J.E. Steif, A characterization of competition graphs of arbitrary digraphs, Discrete Appl. Math. 6 (1983) 323-326, doi: 10.1016/0166-218X(83)90087-2.
[8]	M. Sonntag, H.-M. Teichert, Competition hypergraphs, Discrete Appl. Math. 143 (2004) 324-329, doi: 10.1016/j.dam.2004.02.010.

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