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Two new classes of trees embeddable into hypercubes

Published online by Cambridge University Press:  15 December 2004

Mounira Nekri  and
Abdelhafid Berrachedi
Mounira Nekri
Affiliation:
Centre de Recherche en Information Scientifique et Technique CERIST, 3 rue des frères Aissou, Ben Aknoun Alger, Algeria; [email protected], [email protected].
Abdelhafid Berrachedi
Affiliation:
Faculté des Mathématiques, USTHB BP 32 El Alia, 16111 Bab Ezzouar, Alger, Algeria; [email protected].
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Abstract

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

Type
Research Article
Information
RAIRO - Operations Research , Volume 38 , Issue 4 , October 2004 , pp. 295 - 303
Copyright
© EDP Sciences, 2004

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References

M. Kobeissi, Plongement de graphes dans l'Hypercube. Thèse de Doctorat d'état en informatique. Université Joseph Fourier Grenoble 1 (2001).
F. Harary, M. Lewinter and W. Widulski, On two legged caterpillars which span hypercubes. Cong. Numer. (1988) 103–108.
I. Havel, Embedding certain trees into hypercube, in Recent Advances in graph theory. Academia, Praha (1974) 257–262.
Havel, I. and Liebel, P., One legged caterpillars spans hypercubes. J. Graph Theory 10 (1986) 69–77. CrossRef
I. Havel and P. Liebel, Embedding the dichotomie tree into the cube (Czech with english summary). Cas. Prest. Mat. 97 (1972) 201–205.
I. Havel and J. Moravek, B-valuations of graphs. Czech. Math. J. 22 (1972) 388–351.
Havel, I., On hamiltonian circuits and spanning trees of hypercubes. Cas. prest. Mat. 109 (1984) 135–152.
L. Nebesky, On cubes and dichotomic trees. Cas Prest. Mat. 99 (1974).
Nebesky, L., On quasistars in n-cubes. Cas. Prest. Mat. 109 (1984) 153–156.