Alspach's problem: The case of Hamilton cycles and 5-cycles
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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In this paper, we settle Alspach's problem in the case of Hamilton cycles and 5-cycles; that is, we show that for all odd integers $n\ge 5$ and all nonnegative integers $h$ and $t$ with $hn + 5t = n(n-1)/2$, the complete graph $K_n$ decomposes into $h$ Hamilton cycles and $t$ 5-cycles and for all even integers $n \ge 6$ and all nonnegative integers $h$ and $t$ with $hn + 5t = n(n-2)/2$, the complete graph $K_n$ decomposes into $h$ Hamilton cycles, $t$ 5-cycles, and a $1$-factor. We also settle Alspach's problem in the case of Hamilton cycles and 4-cycles.
Heather Jordon. Alspach's problem: The case of Hamilton cycles and 5-cycles. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/569
@article{10_37236_569,
author = {Heather Jordon},
title = {Alspach's problem: {The} case of {Hamilton} cycles and 5-cycles},
journal = {The electronic journal of combinatorics},
year = {2011},
volume = {18},
number = {1},
doi = {10.37236/569},
zbl = {1217.05186},
url = {http://geodesic.mathdoc.fr/articles/10.37236/569/}
}
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