In this paper it is shown that a complete graph with n vertices has an optimal diagram, i.e., a diagram whose crossing number equals the value of Guy's formula, with a free maximal linear tree and without free hamiltonian cycles for any odd integer n ≥ 7.
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.