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arXiv · 1906.00630

A reduction of the spectrum problem for odd sun systems and the prime case

Marco Buratti·Anita Pasotti·Tommaso Traetta
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Abstract

A $k$-cycle with a pendant edge attached to each vertex is called a $k$-sun. The existence problem for $k$-sun decompositions of $K_v$, with $k$ odd, has been solved only when $k=3$ or $5$. By adapting a method used by Hoffmann, Lindner and Rodger to reduce the spectrum problem for odd cycle systems of the complete graph, we show that if there is a $k$-sun system of $K_v$ ($k$ odd) whenever $v$ lies in the range $2k< v < 6k$ and satisfies the obvious necessary conditions, then such a system exists for every admissible $v\geq 6k$.

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Marco Buratti, Anita Pasotti, Tommaso Traetta. 2019-06-03. A reduction of the spectrum problem for odd sun systems and the prime case. https://doi.org/10.1002/jcd.21751

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