On generalized graphs
On generalized graphs
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DOI：
10.1007/bf01904851
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发表时间：
1965-09
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影响因子：
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通讯作者：
B. Bollobás
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文献类型：
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作者：
B. Bollobás
广义图由n个顶点和k个元组的集合组成。这些顶点（参见TURAN[1]）。下面我们将把这种形像称为k= 2时的边图，通常简单地称为k= 2时的图。一个完全的m图有m个顶点和[k]个k元组。我们说一个图G是m饱和的，如果它不包含完全的m图，但当添加任何新的k元组时失去了这个性质。图~ AN[2]于1941年在边图上证明了以下定理：设n== g (m-1)+ r，其中g、m、r为整数，使得g=> 1, m=> 3， O<= r<= m-1, n~ m，则有n个顶点的m满足边图最多有
A generalizect graph consists of a set of n vertices and a collection of k-tuples. of these vertices (cf. TURAN [1]). In what follows we shall refer to such a configuration as an edge-grapk if k= 2 and, usually, simply as a graph if k> 2. A complete m-graph has mvertices and [k) k-tuples. We say that a graph G is m-saturated if it contains no complete m-graph but loses this property when any new k-tuple is added.Tu~ AN [2] proved the following theorem on edge-graphs in 1941: Let n== g (m-1)+ r, where g, m, and r are integers such that g=> l, m=> 3, O<= r<= m-1, and n~ m. Then an m-satfirated edge-graph of n vertices can have at most