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d-Cube decompositions ofK n/K m

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Abstract

Necessary conditions onn, m andd are given for the existence of an edge-disjoint decomposition ofK n/K m into copies of the graph of ad-dimensional cube. Sufficiency is shown whend=3 and, in some cases, whend=2t. We settle the problem of embedding 3-cube decompositions ofK m into 3-cube decompositions ofK n, wheren≥m.

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Authors and Affiliations

  1. Department of Mathematics, The University of Queensland, 4072, Queensland, Australia

    Peter Adams & Darryn E. Bryant

  2. Department of Mathematics, Illinois State University, 61790-4520, Normal, IL, USA

    Saad I. El-Zanati & Charles Vanden Eynden

Authors
  1. Peter Adams
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  2. Darryn E. Bryant
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  3. Saad I. El-Zanati
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  4. Charles Vanden Eynden
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Additional information

Research of P.A. and D.E.B. supported by Australian Research Council grant A49532750

Research of D.E.B. supported by Australian Research Council grant ARCPDF015G

Research of S.I.E. and C.V.E. supported by Illinois State University Research Office

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Adams, P., Bryant, D.E., El-Zanati, S.I. et al. d-Cube decompositions ofK n/K m . Graphs and Combinatorics 13, 1–7 (1997). https://doi.org/10.1007/BF01202232

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  • DOI: https://doi.org/10.1007/BF01202232

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