Graphs with many r-cliques have large complete r-partite subgraphs
نویسنده
چکیده
We prove that for all r ≥ 2 and c > 0, every G graph of order n with at least cnr cliques of order r contains a complete r-partite graph with each part of size ⌊cr log n⌋ . This result implies a concise form of the Erdős-Stone theorem.
منابع مشابه
2 2 N ov 2 00 7 Graphs with many r - cliques have large complete r - partite subgraphs
Let r ≥ 2 and c > 0. Every graph on n vertices with at least cnr cliques on r vertices contains a complete r-partite subgraph with r − 1 parts of size ⌊cr log n⌋ and one part of size greater than n1−c r−1 . This result implies the Erdős-Stone-Bollobás theorem, the essential quantitative form of the Erdős-Stone theorem.
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تاریخ انتشار 2007