ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2019: 0.755

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Discussiones Mathematicae Graph Theory


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


Martin Sonntag

Faculty of Mathematics and Computer Science
TU Bergakademie Freiberg
Prüferstraße 1, D-09596 Freiberg, Germany

Hanns-Martin Teichert

Institute of Mathematics
University of Lübeck
Wallstraß e 40, D-23560 Lübeck, Germany


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.


[1] J. Bang-Jensen and G. Gutin, Digraphs: theory, algorithms and applications (Springer, London, 2001).
[2] J.E. Cohen, Interval graphs and food webs: a finding and a problem (Rand Corporation Document 17696-PR, Santa Monica, CA, 1968).
[3] K.F. Fraughnaugh, J.R. Lundgren, S.K. Merz, J.S. Maybee and N.J. Pullman, Competition graphs of strongly connected and hamiltonian digraphs, SIAM J. Discrete Math. 8 (1995) 179-185, doi: 10.1137/S0895480191197234.
[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.
[5] J.R. Lundgren, Food webs, competition graphs, competition-common enemy graphs and niche graphs, in: F. Roberts (ed.), Applications of combinatorics and graph theory to the biological and social sciences, IMA 17 (Springer, New York, 1989) 221-243.
[6] F.S. Roberts, Competition graphs and phylogeny graphs, in: L. Lovasz (ed.), Graph theory and combinatorial biology; Proc. Int. Colloqu. Balatonlelle (Hungary) 1996, Bolyai Soc. Math. Studies 7 (Budapest, 1999) 333-362.
[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