- AutorIn
- Lydia Gringmann
- Titel
- Hypergraph Products
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:15-qucosa2-165464
- Schriftenreihe
- Abschluss- und Qualifikationsarbeiten aus der Fakultät für Mathematik und Informatik
- Datum der Einreichung
- 08.02.2010
- Abstract (EN)
- In this work, new definitions of hypergraph products are presented. The main focus is on the generalization of the commutative standard graph products: the Cartesian, the direct and the strong graph product. We will generalize these well-known graph products to products of hypergraphs and show several properties like associativity, commutativity and distributivity w.r.t. the disjoint union of hypergraphs. Moreover, we show that all defined products of simple (hyper)graphs result in a simple (hyper)graph. We will see, for what kind of product the projections into the factors are (at least weak) homomorphisms and for which products there are similar connections between the hypergraph products as there are for graphs. Last, we give a new and more constructive proof for the uniqueness of prime factorization w.r.t. the Cartesian product than in [Studia Sci. Math. Hungar. 2: 285–290 (1967)] and moreover, a product relation according to such a decomposition. That might help to find efficient algorithms for the decomposition of hypergraphs w.r.t. the Cartesian product.
- Freie Schlagwörter (EN)
- hypergraph products, constructive proof, standard graph products
- Klassifikation (DDC)
- 000
- BetreuerIn Hochschule / Universität
- Marc Hellmuth
- Den akademischen Grad verleihende / prüfende Institution
- Universität Leipzig, Leipzig
- Förder- / Projektangaben
- Version / Begutachtungsstatus
- angenommene Version / Postprint / Autorenversion
- URN Qucosa
- urn:nbn:de:bsz:15-qucosa2-165464
- Veröffentlichungsdatum Qucosa
- 20.10.2017
- Dokumenttyp
- Diplomarbeit
- Sprache des Dokumentes
- Englisch
- Deutsch