A perfect one-factorization for \(K_{36}\) (Q1112842)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A perfect one-factorization for \(K_{36}\) |
scientific article; zbMATH DE number 4079471
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A perfect one-factorization for \(K_{36}\) |
scientific article; zbMATH DE number 4079471 |
Statements
A perfect one-factorization for \(K_{36}\) (English)
0 references
1988
0 references
A perfect one-factorization (P1F) of \(K_{2n}\) is such a decomposition of its edge set into one-factors in which every pair of distinct one- factors form a Hamiltonian cycle. P1Fs were known to exist when n or 2n-1 is prime and 2n\(\in \{16,28,50,244,344\}\). In this paper a P1F for \(K_{36}\) is discovered and so the smallest unknown case remains \(K_{40}\).
0 references
complete graph
0 references
edge decomposition
0 references
perfect one-factorization
0 references
0 references
