The Hamilton-Waterloo Problem with $C_4$ and $C_m$ Factors
The Hamilton-Waterloo problem with uniform cycle sizes asks for a $2-$ factorization of the complete graph $K_v$ (for odd {\em v}) or $K_v$ minus a $1-$factor (for even {\em v}) where $r$ of the factors consist of $n-$cycles and $s$ of the factors consist of $m-$cycles with $r+s=\left \lfloor \frac{...
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| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
29-05-2015
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | The Hamilton-Waterloo problem with uniform cycle sizes asks for a $2-$
factorization of the complete graph $K_v$ (for odd {\em v}) or $K_v$ minus a
$1-$factor (for even {\em v}) where $r$ of the factors consist of $n-$cycles
and $s$ of the factors consist of $m-$cycles with $r+s=\left \lfloor
\frac{v-1}{2} \right \rfloor$. In this paper, the Hamilton-Waterloo Problem
with $4-$cycle and $m-$cycle factors for odd $m\geq 3$ is studied and all
possible solutions with a few possible exceptions are determined. |
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| DOI: | 10.48550/arxiv.1505.08121 |