On the Hamilton-Waterloo problem: the case of two cycles sizes of different parity
| Autor: | Melissa S. Keranen, Adrián Pastine |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Ars mathematica contemporanea |
| Popis: | The Hamilton-Waterloo problem asks for a decomposition of the complete graph into $r$ copies of a 2-factor $F_{1}$ and $s$ copies of a 2-factor $F_{2}$ such that $r+s=\left\lfloor\frac{v-1}{2}\right\rfloor$. If $F_{1}$ consists of $m$-cycles and $F_{2}$ consists of $n$ cycles, then we call such a decomposition a $(m,n)-$HWP$(v;r,s)$. The goal is to find a decomposition for every possible pair $(r,s)$. In this paper, we show that for odd $x$ and $y$, there is a $(2^kx,y)-$HWP$(vm;r,s)$ if $\gcd(x,y)\geq 3$, $m\geq 3$, and both $x$ and $y$ divide $v$, except possibly when $1\in\{r,s\}$. Comment: 12 Pages |
| Databáze: | OpenAIRE |
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