The spectrum of maximal sets of one-factors
โ Scribed by Rolf Rees; W.D. Wallis
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 721 KB
- Volume
- 97
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
Rees, R. and W.D. Wallis, The spectrum of maximal sets of one-factors, Discrete Mathematics 97 (1991) 357-369. A set {e} of disjoint one-factors on n vertices is maximal if the complement of the graph IJ 4 has no one-factor. We determine the spectrum of pairs ((n, k): there exists a maximal set of k one-factors on n vertices}.
๐ SIMILAR VOLUMES
We show that the necessary condition m โค k โค 3m -1 that there exists a maximal set of k triangle-factors on 6m โฅ 18 vertices is also sufficient, except possibly when k = m.
We show that the necessary condition m + 1 โค k โค 3m + 1 that there exist a maximal set of k triangle-factors on 6m + 3 โฅ 15 vertices is also sufficient, except possibly when k = m + 1, or when 6m + 3 {45, 57, 69, 81, 93, 237, 261, 309, 333, 381}.