Two new classes of trees embeddable into hypercubes

Mounira Nekri; Abdelhafid Berrachedi

RAIRO - Operations Research (2010)

  • Volume: 38, Issue: 4, page 295-303
  • ISSN: 0399-0559

Abstract

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The problem of embedding graphs into other graphs is much studied in the graph theory. In fact, much effort has been devoted to determining the conditions under which a graph G is a subgraph of a graph H, having a particular structure. An important class to study is the set of graphs which are embeddable into a hypercube. This importance results from the remarkable properties of the hypercube and its use in several domains, such as: the coding theory, transfer of information, multicriteria rule, interconnection networks ... In this paper we are interested in defining two new classes of embedding trees into the hypercube for which the dimension is given.

How to cite

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Nekri, Mounira, and Berrachedi, Abdelhafid. "Two new classes of trees embeddable into hypercubes." RAIRO - Operations Research 38.4 (2010): 295-303. <http://eudml.org/doc/105316>.

@article{Nekri2010,
abstract = { The problem of embedding graphs into other graphs is much studied in the graph theory. In fact, much effort has been devoted to determining the conditions under which a graph G is a subgraph of a graph H, having a particular structure. An important class to study is the set of graphs which are embeddable into a hypercube. This importance results from the remarkable properties of the hypercube and its use in several domains, such as: the coding theory, transfer of information, multicriteria rule, interconnection networks ... In this paper we are interested in defining two new classes of embedding trees into the hypercube for which the dimension is given. },
author = {Nekri, Mounira, Berrachedi, Abdelhafid},
journal = {RAIRO - Operations Research},
language = {eng},
month = {3},
number = {4},
pages = {295-303},
publisher = {EDP Sciences},
title = {Two new classes of trees embeddable into hypercubes},
url = {http://eudml.org/doc/105316},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Nekri, Mounira
AU - Berrachedi, Abdelhafid
TI - Two new classes of trees embeddable into hypercubes
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 4
SP - 295
EP - 303
AB - The problem of embedding graphs into other graphs is much studied in the graph theory. In fact, much effort has been devoted to determining the conditions under which a graph G is a subgraph of a graph H, having a particular structure. An important class to study is the set of graphs which are embeddable into a hypercube. This importance results from the remarkable properties of the hypercube and its use in several domains, such as: the coding theory, transfer of information, multicriteria rule, interconnection networks ... In this paper we are interested in defining two new classes of embedding trees into the hypercube for which the dimension is given.
LA - eng
UR - http://eudml.org/doc/105316
ER -

References

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  1. M. Kobeissi, Plongement de graphes dans l'Hypercube. Thèse de Doctorat d'état en informatique. Université Joseph Fourier Grenoble 1 (2001).  
  2. F. Harary, M. Lewinter and W. Widulski, On two legged caterpillars which span hypercubes. Cong. Numer. (1988) 103–108.  Zbl0692.05023
  3. I. Havel, Embedding certain trees into hypercube, in Recent Advances in graph theory. Academia, Praha (1974) 257–262.  
  4. I. Havel and P. Liebel, One legged caterpillars spans hypercubes. J. Graph Theory10 (1986) 69–77.  Zbl0589.05031
  5. I. Havel and P. Liebel, Embedding the dichotomie tree into the cube (Czech with english summary). Cas. Prest. Mat. 97 (1972) 201–205.  
  6. I. Havel and J. Moravek, B-valuations of graphs. Czech. Math. J. 22 (1972) 388–351.  Zbl0247.05148
  7. I. Havel, On hamiltonian circuits and spanning trees of hypercubes. Cas. prest. Mat.109 (1984) 135–152.  Zbl0544.05057
  8. L. Nebesky, On cubes and dichotomic trees. Cas Prest. Mat.99 (1974).  Zbl0277.05101
  9. L. Nebesky, On quasistars in n-cubes. Cas. Prest. Mat.109 (1984) 153–156.  Zbl0542.05029

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