In 1983 Kleitman and Winston conjectured that the largest coefficient in an n th q-Catalan number is of order O(4 n Γn 3Γ2 ). Assuming its truth, they proved that the total number of n-tournament score sequences is O(4 n Γn 5Γ2 ), thus matching their own lower bound. Our purpose is to confirm the co
On a Conjecture of Kleitman and Lemke
β Scribed by A. Geroldinger
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 161 KB
- Volume
- 44
- Category
- Article
- ISSN
- 0022-314X
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## Abstract The following conjecture of Brualdi and Shen is proven in this paper: let __n__ be partitioned into natural numbers no one of which is greater than (__n__β+β1)β/β2. Then, given any sequence of wins for the players of some tournament among n players, there is a partition of the players i
This article is motivated by a conjecture of Thomassen and Toft on the number s 2 (G) of separating vertex sets of cardinality 2 and the number v 2 (G) of vertices of degree 2 in a graph G belonging to the class G of all 2-connected graphs without nonseparating induced cycles. Let G denote the numbe