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arXiv · 1501.06999

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

Francesca Merola·Tommaso Traetta
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Abstract

It is conjectured that for every pair $(\ell,m)$ of odd integers greater than 2 with $m \equiv 1\; \pmod{\ell}$, 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 $\ell \equiv 1\; \pmod{4}$ and $m \geq \ell^2 -\ell + 1$.

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Francesca Merola, Tommaso Traetta. 2016-03-31. Infinitely many cyclic solutions to the Hamilton-Waterloo problem with odd length cycles. https://arxiv.org/abs/1501.06999

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