# Directed hypergraphs: a tool for researching digraphs and hypergraphs

Hortensia Galeana-Sánchez; Martín Manrique

Discussiones Mathematicae Graph Theory (2009)

- Volume: 29, Issue: 2, page 313-335
- ISSN: 2083-5892

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topHortensia Galeana-Sánchez, and Martín Manrique. "Directed hypergraphs: a tool for researching digraphs and hypergraphs." Discussiones Mathematicae Graph Theory 29.2 (2009): 313-335. <http://eudml.org/doc/270515>.

@article{HortensiaGaleana2009,

abstract = {
In this paper we introduce the concept of directed hypergraph. It is a generalisation of the concept of digraph and is closely related with hypergraphs. The basic idea is to take a hypergraph, partition its edges non-trivially (when possible), and give a total order to such partitions. The elements of these partitions are called levels. In order to preserve the structure of the underlying hypergraph, we ask that only vertices which belong to exactly the same edges may be in the same level of any edge they belong to. Some little adjustments are needed to avoid directed walks within a single edge of the underlying hypergraph, and to deal with isolated vertices.
The concepts of independent set, absorbent set, and transversal set are inherited directly from digraphs.
As a consequence of our results on this topic, we have found both a class of kernel-perfect digraphs with odd cycles and a class of hypergraphs which have a strongly independent transversal set.
},

author = {Hortensia Galeana-Sánchez, Martín Manrique},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {hypergraph; strongly independent set; transversal set; kernel},

language = {eng},

number = {2},

pages = {313-335},

title = {Directed hypergraphs: a tool for researching digraphs and hypergraphs},

url = {http://eudml.org/doc/270515},

volume = {29},

year = {2009},

}

TY - JOUR

AU - Hortensia Galeana-Sánchez

AU - Martín Manrique

TI - Directed hypergraphs: a tool for researching digraphs and hypergraphs

JO - Discussiones Mathematicae Graph Theory

PY - 2009

VL - 29

IS - 2

SP - 313

EP - 335

AB -
In this paper we introduce the concept of directed hypergraph. It is a generalisation of the concept of digraph and is closely related with hypergraphs. The basic idea is to take a hypergraph, partition its edges non-trivially (when possible), and give a total order to such partitions. The elements of these partitions are called levels. In order to preserve the structure of the underlying hypergraph, we ask that only vertices which belong to exactly the same edges may be in the same level of any edge they belong to. Some little adjustments are needed to avoid directed walks within a single edge of the underlying hypergraph, and to deal with isolated vertices.
The concepts of independent set, absorbent set, and transversal set are inherited directly from digraphs.
As a consequence of our results on this topic, we have found both a class of kernel-perfect digraphs with odd cycles and a class of hypergraphs which have a strongly independent transversal set.

LA - eng

KW - hypergraph; strongly independent set; transversal set; kernel

UR - http://eudml.org/doc/270515

ER -

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