ArticleOriginal scientific text
Title
A note on packing of two copies of a hypergraph
Authors 1, 2
Affiliations
- Faculty of Applied Mathematics, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland
- Institute of Mathematics, Polish Academy of Sciences, Św. Tomasza 30, Kraków, Poland
Abstract
A 2-packing of a hypergraph is a permutation σ on V() such that if an edge e belongs to (), then σ (e) does not belong to (). We prove that a hypergraph which does not contain neither empty edge ∅ nor complete edge V() and has at most 1/2n edges is 2-packable. A 1-uniform hypergraph of order n with more than 1/2n edges shows that this result cannot be improved by increasing the size of .
Keywords
packing, hypergraphs
Bibliography
- A. Benhocine and A.P. Wojda, On self-complementation, J. Graph Theory 8 (1985) 335-341, doi: 10.1002/jgt.3190090305.
- B. Bollobás, Extremal Graph Theory (Academic Press, London, 1978).
- D. Burns and S. Schuster, Every (n, n-2) graph is contained in its complement, J. Graph Theory 1 (1977) 277-279, doi: 10.1002/jgt.3190010308.
- M. Woźniak, Embedding graphs of small size, Discrete Applied Math. 51 (1994) 233-241, doi: 10.1016/0166-218X(94)90112-0.
- M. Woźniak, Packing of graphs, Dissertationes Math. 362 (1997) 1-78.
- M. Woźniak, Packing of graphs and permutations - a survey, Discrete Math. 276 (2004) 379-391, doi: 10.1016/S0012-365X(03)00296-6.
- H.P. Yap, Some Topics in Graph Theory, London Math. Society, Lecture Notes Series, Vol. 108 (Cambridge University Press, Cambridge, 1986).
- H.P. Yap, Packing of graphs - a survey, Discrete Math. 72 (1988) 395-404, doi: 10.1016/0012-365X(88)90232-4.
Pages:
45-49
Main language of publication
English
Received
2005-09-05
Accepted
2007-01-12
Published
2007
DOI: 10.7151/dmgt.1343
Exact and natural sciences