Graphs with many r -cliques have large complete r -partite subgraphs
نویسندگان
چکیده
منابع مشابه
Graphs with many r-cliques have large complete r-partite subgraphs
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.
متن کامل2 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.
متن کاملComplete r-partite subgraphs of dense r-graphs
Let r ≥ 3 and (lnn)−1/(r−1) ≤ α ≤ r−3. We show that: Every r-uniform graph on n vertices with at least αnr/r! edges contains a complete r-partite graph with r − 1 parts of size ⌊ α (lnn)1/(r−1) ⌋ and one part of size ⌈ n1−α r−2 ⌉ . This result follows from a more general digraph version: Let U1, . . . , Ur be sets of size n, and M ⊂ U1 × · · · × Ur satisfy |M | ≥ αnr. If the integers s1, . . . ...
متن کاملUnmixed $r$-partite graphs
Unmixed bipartite graphs have been characterized by Ravindra and Villarreal independently. Our aim in this paper is to characterize unmixed $r$-partite graphs under a certain condition, which is a generalization of Villarreal's theorem on bipartite graphs. Also, we give some examples and counterexamples in relevance to this subject.
متن کاملIntegral complete r-partite graphs
A graph is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper, we give a useful sufficient and necessary condition for complete r-partite graphs to be integral, from which we can construct infinite many new classes of such integral graphs. It is proved that the problem of finding such integral graphs is equivalent to the problem of solving some Diophantin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2008
ISSN: 0024-6093
DOI: 10.1112/blms/bdm093