Pairwise Compatible Hamilton Decompositions ofKn

In this paper we prove that there are either 2k−2 or 2k−1 pairwise compatible Hamilton path decompositions ofK2k. In the case ofK4, there exactly 2 compatible Hamilton path decompositions. We also find (different) lower bounds on the number of pairwise compatible Hamilton decompositions ofK4m+1andK4m+3.