Graph factorization, general triple systems, and cyclic triple systems
Copyright policy )Graph factorization, general triple systems, and cyclic triple systems
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.
- DigiZeitschriften Germany
- University of Waterloo Canada
- University of Manitoba Canada
Steiner triple system, incidence matrix, cyclic triple system, Article, Combinatorial aspects of block designs, one-factorization, 510.mathematics, Steiner systems in finite geometry, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), Research exposition (monographs, survey articles) pertaining to combinatorics, Combinatorial aspects of matrices (incidence, Hadamard, etc.)
Steiner triple system, incidence matrix, cyclic triple system, Article, Combinatorial aspects of block designs, one-factorization, 510.mathematics, Steiner systems in finite geometry, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), Research exposition (monographs, survey articles) pertaining to combinatorics, Combinatorial aspects of matrices (incidence, Hadamard, etc.)
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