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;
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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/166067
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