A Note on Uniquely Embeddable Forests

Justyna Otfinowska; Mariusz Woźniak

Discussiones Mathematicae Graph Theory (2013)

  • Volume: 33, Issue: 1, page 193-201
  • ISSN: 2083-5892

Abstract

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Let F be a forest of order n. It is well known that if F 6= Sn, a star of order n, then there exists an embedding of F into its complement F. In this note we consider a problem concerning the uniqueness of such an embedding.

How to cite

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Justyna Otfinowska, and Mariusz Woźniak. "A Note on Uniquely Embeddable Forests." Discussiones Mathematicae Graph Theory 33.1 (2013): 193-201. <http://eudml.org/doc/267848>.

@article{JustynaOtfinowska2013,
abstract = {Let F be a forest of order n. It is well known that if F 6= Sn, a star of order n, then there exists an embedding of F into its complement F. In this note we consider a problem concerning the uniqueness of such an embedding.},
author = {Justyna Otfinowska, Mariusz Woźniak},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {packings of graphs; uniquely embeddable graphs},
language = {eng},
number = {1},
pages = {193-201},
title = {A Note on Uniquely Embeddable Forests},
url = {http://eudml.org/doc/267848},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Justyna Otfinowska
AU - Mariusz Woźniak
TI - A Note on Uniquely Embeddable Forests
JO - Discussiones Mathematicae Graph Theory
PY - 2013
VL - 33
IS - 1
SP - 193
EP - 201
AB - Let F be a forest of order n. It is well known that if F 6= Sn, a star of order n, then there exists an embedding of F into its complement F. In this note we consider a problem concerning the uniqueness of such an embedding.
LA - eng
KW - packings of graphs; uniquely embeddable graphs
UR - http://eudml.org/doc/267848
ER -

References

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  1. [1] 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[Crossref] Zbl0387.05020
  2. [2] 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[Crossref] Zbl0375.05046
  3. [3] D. Burns and S. Schuster, Embedding (n, n−1) graphs in their complements, Israel J. Math. 30 (1978) 313-320. doi:10.1007/BF02761996[Crossref] 
  4. [4] B. Ganter, J. Pelikan and L. Teirlinck, Small sprawling systems of equicardinal sets, Ars Combin. 4 (1977) 133-142. Zbl0418.05003
  5. [5] 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[Crossref] Zbl0417.05037
  6. [6] J. Otfinowska and M. Woźniak, A note on uniquely embeddable forests, Preprint MD (www.ii.uj.edu.pl/preMD/) 046 (2010). Zbl1291.05162
  7. [7] M. Woźniak, Embedding graphs of small size, Discrete Applied Math. 51 (1994) 233-241. doi:10.1016/0166-218X(94)90112-0[Crossref] 
  8. [8] M. Woźniak, Packing three trees, Discrete Math. 150 (1996) 393-402. doi:10.1016/0012-365X(95)00204-A[Crossref] 
  9. [9] M. Woźniak, A note on uniquely embeddable graphs, Discuss. Math. Graph Theory 18 (1998) 15-21. doi:10.7151/dmgt.1060[Crossref] Zbl0915.05050
  10. [10] M. Woźniak, Packing of graphs-some recent results and trends, Studies, Math. Series 16 (2003) 115-120. Zbl1049.05513
  11. [11] M. Woźniak, Packing of graphs and permutation-a survey, Discrete Math. 276 (2004) 379-391. doi:10.1016/S0012-365X(03)00296-6[Crossref] 
  12. [12] M. Woźniak, A note on uniquely embeddable cycles, Preprint MD (www.ii.uj.edu.pl/preMD/) 047 (2010). 
  13. [13] H.P. Yap, Packing of graphs-a survey, Discrete Math. 72 (1988) 395-404. doi:10.1016/0012-365X(88)90232-4[Crossref] 

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