Digraph extremal problems, hypergraph extremal problems, and the densities of graph structures
نویسندگان
چکیده
منابع مشابه
Extremal Hypergraph Problems and the Regularity Method
Szemerédi’s regularity lemma asserts that every graph can be decomposed into relatively few random-like subgraphs. This random-like behavior enables one to find and enumerate subgraphs of a given isomorphism type, yielding the so-called counting lemma for graphs. The combined application of these two lemmas is known as the regularity method for graphs and has proved useful in graph theory, comb...
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Notation. Given a graph, hypergraph Gn, . . . , the upper index always denotes the number of vertices, e(G), v(G) and χ(G) denote the number of edges, vertices and the chromatic number of G respectively. Given a family L of graphs, hypergraphs, ex(n,L) denotes the maximum number of edges (hyperedges) a graph (hypergraph)Gn of order n can have without containing subgraphs (subhypergraphs) from L...
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We present alternative proofs of density versions of some combinatorial partition theorems originally obtained by H. Furstenberg and Y. Katznelson. These proofs are based on an extremal hypergraph result which was recently independently obtained by W. T. Gowers and B. Nagle, V. Rödl, M. Schacht, J. Skokan by extending Szemerédi’s regularity lemma to hypergraphs.
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The main result of this paper is that for a special, but rather wide class of "sample graphs", the extremal graphs, i.e, the graphs of n vertices without subgraphs isomorphic to the sample graph and having maximum number of edges under this condition, have very simple and sYmmetric structure. This result remains valid even in the case when the' condition "the graph does not contain the sample g...
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A set P of graphs is termed hereditary property if and only if it contains all subgraphs of any graph G belonging to P. A graph is said to be maximal with respect to a hereditary property P (shortly P-maximal) whenever it belongs to P and none of its proper supergraphs of the same order has the property P. A graph is P-extremal if it has a the maximum number of edges among all P-maximal graphs ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1984
ISSN: 0012-365X
DOI: 10.1016/0012-365x(84)90178-x