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Graph factorization, general triple systems, and cyclic triple systems

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Abstract

In this self-contained exposition, results are developed concerning one-factorizations of complete graphs, and incidence matrices are used to turn these factorization results into embedding theorems on Steiner triple systems. The result is a constructive graphical proof that a Steiner triple system exists for any order congruent to 1 or 3 modulo 6. A pairing construction is then introduced to show that one can also obtain triple systems which are cyclically generated.

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Authors and Affiliations

  1. Department of Computer Science, University of Manitoba, R3T 2N2, Winnipeg, Manitoba, Canada

    R. G. Stanton & I. P. Goulden

  2. Department of Statistics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    R. G. Stanton & I. P. Goulden

  3. CSIRO, Melbourne, Australia

    R. G. Stanton & I. P. Goulden

Authors
  1. R. G. Stanton
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  2. I. P. Goulden
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Stanton, R.G., Goulden, I.P. Graph factorization, general triple systems, and cyclic triple systems. Aeq. Math. 22, 1–28 (1981). https://doi.org/10.1007/BF02190154

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  • DOI: https://doi.org/10.1007/BF02190154

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