In this paper we prove that there are either 2k&2 or 2k&1 pairwise compatible Hamilton path decompositions of K 2k . In the case of K 4 , there exactly 2 compatible Hamilton path decompositions. We also find (different) lower bounds on the number of pairwise compatible Hamilton decompositions of K 4m+1 and K 4m+3 .
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.