科研之友
微信
新浪微博
Facebook
分享链接
摘要
Thomason and Chung, Graham and Wilson were the first to systematically investigate properties of quasirandom graphs. They have stated several quite disparate graph properties - such as having uniform edge distribution or containing a prescribed number of certain subgraphs - and proved that these properties are equivalent in a deterministic sense. Simonovits and Ss introduced a hereditary property (which we call S) stating the following: for a small fixed graph L, a graph G on n vertices is said to have the property S if for every set X aS dagger V(G), the number of labeled copies of L in G[X] (the subgraph of G induced by the vertices of X) is given by 2(-e(L))|X| (upsilon(L)) + o(n (upsilon(L))). They have shown that S is equivalent to the other quasirandom properties. In this paper we give a natural extension of the result of Simonovits and Ss to k-uniform hypergraphs, answering a question of Conlon et al. Our approach also yields an alternative, and perhaps simpler, proof of one of their theorems.
- 出版日期2011-3
