Symmetric Hamilton Cycle Decompositions of Complete Graphs Minus a 1-Factor
نویسندگان
چکیده
Let n ≥ 2 be an integer. The complete graph Kn with a 1-factor F removed has a decomposition into Hamilton cycles if and only if n is even. We show that Kn − F has a decomposition into Hamilton cycles which are symmetric with respect to the 1-factor F if and only if n ≡ 2, 4 mod 8. We also show that the complete bipartite graph Kn,n has a symmetric Hamilton cycle decomposition if and only if n is even, and that if F is a 1-factor of Kn,n, then Kn,n − F has a symmetric Hamilton cycle decomposition if and only if n is odd.
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