Infinitely many cyclic solutions to the Hamilton-Waterloo problem with odd length cycles

Abstract

It is conjectured that for every pair $(\ell ,m)$ of odd integers greater than 2 with $m\equiv 1(\mathrm{mod}\ell )$, there exists a cyclic two-factorization of $K_{\ell m}$ having exactly $(m-1)/2$ factors of type ${\ell }^m$ and all the others of type $m^{\ell }$. The authors prove the conjecture in the affirmative when $\ell \equiv 1(\mathrm{mod}4)$ and $m\ge {\ell }^2-\ell +1$.

31 pages

References in corpus (2)

• Octahedral, dicyclic and special linear solutions of some unsolved Hamilton-Waterloo problems
• On the Hamilton-Waterloo Problem with odd orders