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Decompositions of $n$-Cube into $2^mn$-Cycles
| Content Provider | Semantic Scholar |
|---|---|
| Author | Tapadia, Sanjay Waphare, B. N. Borse, Y. M. |
| Copyright Year | 2018 |
| Abstract | It is known that the $n$-dimensional hypercube $Q_n,$ for $n$ even, has a decomposition into $k$-cycles for $k=n, 2n,$ $2^l$ with $2 \leq l \leq n.$ In this paper, we prove that $Q_n$ has a decomposition into $2^mn$-cycles for $n \geq 2^m.$ As an immediate consequence of this result, we get path decompositions of $Q_n$ as well. This gives a partial solution to a conjecture posed by Ramras and also, it solves some special cases of a conjecture due to Erde. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/1804.01243v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
