×

zbMATH — the first resource for mathematics

The resolution of the anti-Pasch conjecture. (English) Zbl 0959.05016
The authors settle the long-standing conjecture (going back to Erdős (1976) and Brouwer (1977)) that for each \(v\equiv 1\) or \(3\) (mod \(6\)), \(v\neq 7,\;13\), there exists a Steiner triple system of order \(v\) that does not contain any Pasch configuration.

MSC:
05B07 Triple systems
PDF BibTeX Cite
Full Text: DOI
References:
[1] Steiner triple systems without forbidden subconfigurations, Mathematisch Centrum Amsterdam, ZW, (1977), 104/77. · Zbl 0367.05011
[2] Colbourn, Graphs and Combinatorics 10 pp 215– (1994)
[3] and Combinatorial designs in communications, Surveys in Combinatorics, 1999 (LMS Lecture Note Series, 267), Cambridge University Press, (1999), 37-100.
[4] Erd?s, Creation in Math. 9 pp 25– (1976)
[5] Grannell, Journal of Combinatorial Designs website (1999)
[6] Griggs, J. Combin. Math. Combin. Comput. 13 pp 129– (1993)
[7] Griggs, J. Combin. Inf. Syst. Sci. 15 pp 79– (1990)
[8] Kotzig, Utilitas Math. 7 pp 287– (1975)
[9] Kotzig, Discrete Math. 16 pp 263– (1975)
[10] Ling, J. London Math. Soc.
[11] Mathon, Ars Comb. 15 pp 3– (1983)
[12] McLeish, Utilitas Math. 8 pp 41– (1975)
[13] Steiner triple systems and cycle structure, Ph.D. thesis, University of Central Lancashire, 1999.
[14] Stinson, Ann. Discrete Math. 26 pp 321– (1985)
[15] Stinson, Math. Comput. 44 pp 533– (1985)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.