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Packing of nonuniform hypergraphs - product and sum of sizes conditions

Paweł Naroski (2009)

Discussiones Mathematicae Graph Theory

Hypergraphs H ₁ , . . . , H N of order n are mutually packable if one can find their edge disjoint copies in the complete hypergraph of order n. We prove that two hypergraphs are mutually packable if the product of their sizes satisfies some upper bound. Moreover we show that an arbitrary set of the hypergraphs is mutually packable if the sum of their sizes is sufficiently small.

Packing the Hypercube

David Offner (2014)

Discussiones Mathematicae Graph Theory

Let G be a graph that is a subgraph of some n-dimensional hypercube Qn. For sufficiently large n, Stout [20] proved that it is possible to pack vertex- disjoint copies of G in Qn so that any proportion r < 1 of the vertices of Qn are covered by the packing. We prove an analogous theorem for edge-disjoint packings: For sufficiently large n, it is possible to pack edge-disjoint copies of G in Qn so that any proportion r < 1 of the edges of Qn are covered by the packing.

Pattern hypergraphs.

Dvořák, Zdeněk, Kára, Jan, Král', Daniel, Pangrác, Ondřej (2010)

The Electronic Journal of Combinatorics [electronic only]

Platonic hypermaps.

Breda d'Azevedo, Antonio J., Jones, Gareth A. (2001)

Beiträge zur Algebra und Geometrie

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