Discrete mathematics and its applications· 2013· Book chapter
Topological Graph Theory
- 256citations
- 2013year
Short summary
This paper proves that in a tournament with 799 teams where every pair plays once, there must exist two disjoint groups of 7 teams each (A and B) where every team in A defeated every team in B.
AI-generated from the title and abstract; the full text is not read.
Key points
- A tournament with 799 teams is considered, where each pair plays exactly once.
- The existence of two disjoint 7-team groups, A and B, is proven.
- In these groups, every team from A defeated every team from B.
- A probabilistic method, using random sampling, is employed in the proof.
AI-generated from the title and abstract; the full text is not read.
Abstract
2. (Iran Team Selection Test 2008/6) Suppose 799 teams participate in a tournament in which every pair of teams plays against each other exactly once. Prove that there exist two disjoint groups A and B of 7 teams each such that every team from A defeated every team from B. Solution: SampleA as a random 7-set. LetX be the number of guys that are totally dominated byA. Letting dv denote the in-degree of v, we have E [X] = ∑
The authors' abstract, as published at the source. Discrete mathematics and its applications, 2013 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics