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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- [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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