We prove that in every cyclic cycle-decomposition of $K_{2n} − I$ (the cocktail party graph of order 2n) the number of cycle-orbits of odd length must have the same parity of n(n − 1)/2. This gives, as corollaries, some useful non-existence results one of which allows to determine when the two table Oberwolfach Problem OP(3,2l) admits a 1-rotational solution.
A non-existence result on cyclic cycle decompositions of the cocktail party graph / Buratti, Marco; Rinaldi, G.. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - 309 / 2009:(2009), pp. 4722-4726.
A non-existence result on cyclic cycle decompositions of the cocktail party graph
BURATTI, Marco;
2009
Abstract
We prove that in every cyclic cycle-decomposition of $K_{2n} − I$ (the cocktail party graph of order 2n) the number of cycle-orbits of odd length must have the same parity of n(n − 1)/2. This gives, as corollaries, some useful non-existence results one of which allows to determine when the two table Oberwolfach Problem OP(3,2l) admits a 1-rotational solution.File allegati a questo prodotto
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