A note on careful packing of a graph

M. Woźniak

Discussiones Mathematicae Graph Theory (1995)

  • Volume: 15, Issue: 1, page 43-50
  • ISSN: 2083-5892

Abstract

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Let G be a simple graph of order n and size e(G). It is well known that if e(G) ≤ n-2, then there is an edge-disjoint placement of two copies of G into Kₙ. We prove that with the same condition on size of G we have actually (with few exceptions) a careful packing of G, that is an edge-disjoint placement of two copies of G into Kₙ∖Cₙ.

How to cite

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M. Woźniak. "A note on careful packing of a graph." Discussiones Mathematicae Graph Theory 15.1 (1995): 43-50. <http://eudml.org/doc/270510>.

@article{M1995,
abstract = {Let G be a simple graph of order n and size e(G). It is well known that if e(G) ≤ n-2, then there is an edge-disjoint placement of two copies of G into Kₙ. We prove that with the same condition on size of G we have actually (with few exceptions) a careful packing of G, that is an edge-disjoint placement of two copies of G into Kₙ∖Cₙ.},
author = {M. Woźniak},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {pucking of graphs; careful packing},
language = {eng},
number = {1},
pages = {43-50},
title = {A note on careful packing of a graph},
url = {http://eudml.org/doc/270510},
volume = {15},
year = {1995},
}

TY - JOUR
AU - M. Woźniak
TI - A note on careful packing of a graph
JO - Discussiones Mathematicae Graph Theory
PY - 1995
VL - 15
IS - 1
SP - 43
EP - 50
AB - Let G be a simple graph of order n and size e(G). It is well known that if e(G) ≤ n-2, then there is an edge-disjoint placement of two copies of G into Kₙ. We prove that with the same condition on size of G we have actually (with few exceptions) a careful packing of G, that is an edge-disjoint placement of two copies of G into Kₙ∖Cₙ.
LA - eng
KW - pucking of graphs; careful packing
UR - http://eudml.org/doc/270510
ER -

References

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  1. [1] B. Bollobás, Extremal Graph Theory (Academic Press, London, 1978). 
  2. [2] B. Bollobás and S.E. Eldridge, Packings of graphs and applications to computational complexity, J. Combin Theory (B) 25 (1978) 105-124, doi: 10.1016/0095-8956(78)90030-8. Zbl0387.05020
  3. [3] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, (North-Holland, New York, 1976). Zbl1226.05083
  4. [4] D. Burns and S. Schuster, Every (p,p-2)- graph is contained in its complement, J. Graph Theory 1 (1977) 277-279, doi: 10.1002/jgt.3190010308. Zbl0375.05046
  5. [5] D. Burns and S. Schuster, Embedding (n,n-1)- graphs in their complements, Israel J. Math. 30 (1978) 313-320, doi: 10.1007/BF02761996. Zbl0379.05023
  6. [6] B. Ganter, J. Pelikan and L. Teirlinck, Small sprawling systems of equicardinal sets, Ars Combinatoria 4 (1977) 133-142. Zbl0418.05003
  7. [7] N. Sauer and J. Spencer, Edge disjoint placement of graphs, J. Combin Theory (B) 25 (1978) 295-302, doi: 10.1016/0095-8956(78)90005-9. Zbl0417.05037
  8. [8] M. Woźniak, Embedding of graphs in the complements of their squares, in: J. Nesset ril and M. Fiedler, eds, Fourth Czechoslovakian Symp. on Combinatorics, Graphs and Complexity, (Elsevier Science Publishers B.V.,1992) 345-349. Zbl0767.05046
  9. [9] M. Woźniak, Embedding graphs of small size, Discrete Applied Math. 51 (1994) 233-241, doi: 10.1016/0166-218X(94)90112-0. Zbl0807.05025
  10. [10] M. Woźniak and A.P. Wojda, Triple placement of graphs, Graphs and Combinatorics 9 (1993) 85-91, doi: 10.1007/BF01195330. Zbl0817.05034
  11. [11] H.P. Yap, Some Topics In Graph Theory (London Mathematical Society, Lectures Notes Series 108, Cambridge University Press, Cambridge 1986). Zbl0588.05002
  12. [12] 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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