Year: 2026
Type: preprint
Abstract: It is shown that, as $n\to\infty$, the logarithm of the number of decompositions into cycles of the $n$-dimensional Boolean cube $E^n$ is \[ 2^n(\ln n-1+o(1)), \] and the logarithm of the number of Hamiltonian cycles in $E^n$ is at least \[ 2^{n-1}(\ln n-1+o(1)). \] It is proved that, in $E^n$, every perfect matching whose edges belong to at most $k$ directions can be extended to a Hamiltonian cycle for every $n\geq n_0(k)$.
Source: arXiv (Cornell University)
Authors: Perezhogin, A. L., Potapov, V. N.
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221081866