A note on packing of two copies of a hypergraph

Monika Pilśniak; Mariusz Woźniak

Discussiones Mathematicae Graph Theory (2007)

  • Volume: 27, Issue: 1, page 45-49
  • ISSN: 2083-5892

Abstract

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A 2-packing of a hypergraph 𝓗 is a permutation σ on V(𝓗) such that if an edge e belongs to 𝓔(𝓗), then σ (e) does not belong to 𝓔(𝓗). We prove that a hypergraph which does not contain neither empty edge ∅ nor complete edge V(𝓗) 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 𝓗.

How to cite

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Monika Pilśniak, and Mariusz Woźniak. "A note on packing of two copies of a hypergraph." Discussiones Mathematicae Graph Theory 27.1 (2007): 45-49. <http://eudml.org/doc/270724>.

@article{MonikaPilśniak2007,
abstract = { A 2-packing of a hypergraph 𝓗 is a permutation σ on V(𝓗) such that if an edge e belongs to 𝓔(𝓗), then σ (e) does not belong to 𝓔(𝓗). We prove that a hypergraph which does not contain neither empty edge ∅ nor complete edge V(𝓗) 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 𝓗. },
author = {Monika Pilśniak, Mariusz Woźniak},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {packing; hypergraphs},
language = {eng},
number = {1},
pages = {45-49},
title = {A note on packing of two copies of a hypergraph},
url = {http://eudml.org/doc/270724},
volume = {27},
year = {2007},
}

TY - JOUR
AU - Monika Pilśniak
AU - Mariusz Woźniak
TI - A note on packing of two copies of a hypergraph
JO - Discussiones Mathematicae Graph Theory
PY - 2007
VL - 27
IS - 1
SP - 45
EP - 49
AB - A 2-packing of a hypergraph 𝓗 is a permutation σ on V(𝓗) such that if an edge e belongs to 𝓔(𝓗), then σ (e) does not belong to 𝓔(𝓗). We prove that a hypergraph which does not contain neither empty edge ∅ nor complete edge V(𝓗) 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 𝓗.
LA - eng
KW - packing; hypergraphs
UR - http://eudml.org/doc/270724
ER -

References

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  1. [1] A. Benhocine and A.P. Wojda, On self-complementation, J. Graph Theory 8 (1985) 335-341, doi: 10.1002/jgt.3190090305. Zbl0587.05054
  2. [2] B. Bollobás, Extremal Graph Theory (Academic Press, London, 1978). 
  3. [3] 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. Zbl0375.05046
  4. [4] M. Woźniak, Embedding graphs of small size, Discrete Applied Math. 51 (1994) 233-241, doi: 10.1016/0166-218X(94)90112-0. Zbl0807.05025
  5. [5] M. Woźniak, Packing of graphs, Dissertationes Math. 362 (1997) 1-78. 
  6. [6] M. Woźniak, Packing of graphs and permutations - a survey, Discrete Math. 276 (2004) 379-391, doi: 10.1016/S0012-365X(03)00296-6. Zbl1031.05041
  7. [7] H.P. Yap, Some Topics in Graph Theory, London Math. Society, Lecture Notes Series, Vol. 108 (Cambridge University Press, Cambridge, 1986). Zbl0588.05002
  8. [8] H.P. Yap, Packing of graphs - a survey, Discrete Math. 72 (1988) 395-404, doi: 10.1016/0012-365X(88)90232-4. Zbl0685.05036

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