On High-Dimensional Acyclic Tournaments
On High-Dimensional Acyclic Tournaments
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关于高维非循环锦标赛
DOI：
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发表时间：
2013
影响因子：
0.8
通讯作者：
Avraham Morgenstern
中科院分区：
文献类型：
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作者：
N. Linial;Avraham Morgenstern
我们研究了一个异步（又名及其及时的）概念的高维模拟，我们证明，每$ n $$ n $ n-vertex $$ d $$ d-d-di-n-n-n-n-d-n-n-d-n-n-d-n-n-v-n-v-n-vertional锦标赛都包含$$ omega（log ^{1/d} n）$$$ω（log1/dn）顶点和顶点和顶点和顶点的异步子游戏界限很紧张在高维锦标赛中，其他各种无环的概念之间的关系包括组合，几何和拓扑概念。
We study a high-dimensional analog for the notion of an acyclic (aka transitive) tournament. We give upper and lower bounds on the number of $$d$$d-dimensional $$n$$n-vertex acyclic tournaments. In addition, we prove that every $$n$$n-vertex $$d$$d-dimensional tournament contains an acyclic subtournament of $$Omega (log ^{1/d}n)$$Ω(log1/dn) vertices and the bound is tight. This statement for tournaments (i.e., the case $$d=1$$d=1) is a well-known fact. We indicate a connection between acyclic high-dimensional tournaments and Ramsey numbers of hypergraphs. We investigate as well the inter-relations among various other notions of acyclicity in high-dimensional tournaments. These include combinatorial, geometric and topological concepts.