# Competition hypergraphs of digraphs with certain properties II. Hamiltonicity

Martin Sonntag; Hanns-Martin Teichert

Discussiones Mathematicae Graph Theory (2008)

- Volume: 28, Issue: 1, page 23-34
- ISSN: 2083-5892

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topMartin Sonntag, and Hanns-Martin Teichert. "Competition hypergraphs of digraphs with certain properties II. Hamiltonicity." Discussiones Mathematicae Graph Theory 28.1 (2008): 23-34. <http://eudml.org/doc/270461>.

@article{MartinSonntag2008,

abstract = {If D = (V,A) is a digraph, its competition hypergraph (D) has vertex set V and e ⊆ V is an edge of (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 (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].},

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

journal = {Discussiones Mathematicae Graph Theory},

keywords = {hypergraph; competition graph; hamiltonian digraph; competition hypergraph; Hamiltonian digraph; food web},

language = {eng},

number = {1},

pages = {23-34},

title = {Competition hypergraphs of digraphs with certain properties II. Hamiltonicity},

url = {http://eudml.org/doc/270461},

volume = {28},

year = {2008},

}

TY - JOUR

AU - Martin Sonntag

AU - Hanns-Martin Teichert

TI - Competition hypergraphs of digraphs with certain properties II. Hamiltonicity

JO - Discussiones Mathematicae Graph Theory

PY - 2008

VL - 28

IS - 1

SP - 23

EP - 34

AB - If D = (V,A) is a digraph, its competition hypergraph (D) has vertex set V and e ⊆ V is an edge of (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 (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].

LA - eng

KW - hypergraph; competition graph; hamiltonian digraph; competition hypergraph; Hamiltonian digraph; food web

UR - http://eudml.org/doc/270461

ER -

## References

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- [10] J.R. Lundgren and J.S. Maybee, A characterization of graphs of competition number m, Discrete Appl. Math. 6 (1983) 319-322, doi: 10.1016/0166-218X(83)90086-0. Zbl0521.05058
- [11] 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
- [12] F.S. Roberts and 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
- [13] M. Sonntag and 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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