A CONSTRUCTION OF ONE-FACTORIZATION

Title & Authors
A CONSTRUCTION OF ONE-FACTORIZATION
Choi, Yoon-Young; Kim, Sang-Mok; Lim, Seon-Ju; Park, Bong-Joo;

Abstract
In this paper, we construct one-factorizations of given complete graphs of even order. These constructions partition the edges of the complete graph into one-factors and triples. Our new constructions of one-factors and triples can be applied to a recursive construction of Steiner triple systems for all possible orders $\small{{\geq}}$15.
Keywords
one-factorizations;Steiner triple systems;
Language
English
Cited by
References
1.
L. D. Andersen, Factorizations of graphs, in : CRC Handbook of Combinatorial Designs, C. J. Colbourn and J. H. Dinitz (eds), CRC Press, Boca Raton, FL, 1996, 653-667

2.
C. J. Colbourn and A. Rosa, Triple Systems, Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 1999

3.
J. Doyen and R. M. Wilson, Embeddings of Steiner triple systems, Discrete Math. 5 (1973), 229-239

4.
A. Hartman, Tripling quadruple systems, Ars Combin. 10 (1980), 255-309

5.
E. Mendelsohn and A. Rosa, One-factorizations of the complete graph-a survey, J. Graph Theory 9 (1985), no. 1, 43-65

6.
M. Reiss, Uber eine Steinersche combinatorische Aufgabe, welche im 45sten Banden dises Journals, Seite 181, gestellt worden ist, J. Reine Angew Math. 65 (1859), 226-244

7.
R. G. Stanton and I. P. Goulden, Graph factorization, general triple systems, and cyclic triple systems, Aequationes Math. 22 (1981), no. 1, 1-28

8.
G. Stern and H. Lenz, Steiner triple systems with given subspaces; another proof of the Doyen-Wilson-theorem, Boll. Un. Mat. Ital. A (5) 17 (1980), no. 1, 109-114

9.
W. D. Wallis, One-factorizations of the complete graph, in : Contemporary Design Theory : A Collection of Surveys, J. H. Dinitz and D. R. Stinson (eds), Wiley, New York, 1992, 593-631

10.
W. D. Wallis, One-factorizations, Mathematics and its Applications, 390. Kluwer Academic Publishers Group, Dordrecht, 1997