Taiwanese Journal of Mathematics

FROM STEINER TRIPLE SYSTEMS TO 3-SUN SYSTEMS

Chin-Mei Fu, Nan-Hua Jhuang, Yuan-Lung Lin, and Hsiao-Ming Sung

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Abstract

An $n$-$sun$ is the graph with $2n$ vertices consisting of an $n$-cycle with $n$ pendent edges which form a 1-factor. In this paper we show that the necessary and sufficient conditions for the decomposition of complete tripartite graphs with at least two partite sets having the same size into $3$-suns and give another construction to get a $3$-sun system of order $n$, for $n\equiv 0,1,4,9$ (mod 12). In the construction we metamorphose a Steiner triple system into a $3$-sun system. We then embed a cyclic Steiner triple system of order $n$ into a $3$-sun system of order $2n-1$, for $n\equiv 1$ (mod 6).

Article information

Source
Taiwanese J. Math., Volume 16, Number 2 (2012), 531-543.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406600

Digital Object Identifier
doi:10.11650/twjm/1500406600

Mathematical Reviews number (MathSciNet)
MR2892897

Zentralblatt MATH identifier
1242.05036

Subjects
Primary: 05B30: Other designs, configurations [See also 51E30]

Keywords
Steiner triple system 3-sun 3-sun system cyclic decomposition

Citation

Fu, Chin-Mei; Jhuang, Nan-Hua; Lin, Yuan-Lung; Sung, Hsiao-Ming. FROM STEINER TRIPLE SYSTEMS TO 3-SUN SYSTEMS. Taiwanese J. Math. 16 (2012), no. 2, 531--543. doi:10.11650/twjm/1500406600. https://projecteuclid.org/euclid.twjm/1500406600


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References

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