# Competition hypergraphs of digraphs with certain properties I. Strong connectedness

Martin Sonntag; Hanns-Martin Teichert

Discussiones Mathematicae Graph Theory (2008)

- Volume: 28, Issue: 1, page 5-21
- ISSN: 2083-5892

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topMartin Sonntag, and Hanns-Martin Teichert. "Competition hypergraphs of digraphs with certain properties I. Strong connectedness." Discussiones Mathematicae Graph Theory 28.1 (2008): 5-21. <http://eudml.org/doc/270260>.

@article{MartinSonntag2008,

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].},

author = {Martin Sonntag, Hanns-Martin Teichert},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {hypergraph; competition graph; strong component; competition hypergraph; strongly connected component; food web},

language = {eng},

number = {1},

pages = {5-21},

title = {Competition hypergraphs of digraphs with certain properties I. Strong connectedness},

url = {http://eudml.org/doc/270260},

volume = {28},

year = {2008},

}

TY - JOUR

AU - Martin Sonntag

AU - Hanns-Martin Teichert

TI - Competition hypergraphs of digraphs with certain properties I. Strong connectedness

JO - Discussiones Mathematicae Graph Theory

PY - 2008

VL - 28

IS - 1

SP - 5

EP - 21

AB - 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].

LA - eng

KW - hypergraph; competition graph; strong component; competition hypergraph; strongly connected component; food web

UR - http://eudml.org/doc/270260

ER -

## References

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- [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. Zbl0830.05035
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- [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. Zbl0924.05032
- [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. Zbl0521.05059
- [8] M. Sonntag, H.-M. Teichert, Competition hypergraphs, Discrete Appl. Math. 143 (2004) 324-329, doi: 10.1016/j.dam.2004.02.010. Zbl1056.05103

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