منابع مشابه
On unavoidable hypergraphs
A r-uniform hypergraph H (or a r-graph, for short) is a collection E= E(H) of r-element subsets (called edges) of a set V = V(H) (called vertices) . We say a r-graph H is (n, e)-unavoidable if every r-graph with n vertices and e edges must contain H . In this paper we investigate the largest possible number of edges in an (n, e)-unavoidable 3-graph for fixed n and e. We also study the structure...
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A classical result of Erdős and Hajnal claims that for any integers k, r, g ≥ 2 there is an r-uniform hypergraph of girth at least g with chromatic number at least k. This implies that there are sparse hypergraphs such that in any coloring of their vertices with at most k − 1 colors there is a monochromatic hyperedge. We show that for any integers r, g ≥ 2 there is an r-uniform hypergraph of gi...
متن کاملOn unavoidable graphs
How many edges can be in a graph which is forced to be contained in every graph on n verti-ces and e edges? 1n this paper we obtain bounds which are in many cases asymptotically best possible. A well-known theorem of Turán [10,11] asserts that every graph on n vertices and e edges must contain a complete subgraph on m vertices if e~2(m 1)(n-rL)+(2) where r satisfies r-n (mod m-1) and In this pa...
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A set of words over a finite alphabet is called an unavoidable set if every word of sufficiently long length must contain some word from this set as a subword. Motivated by a theorem from automata theory, we introduce the notion of an almost unavoidable set and prove certain asymptotic estimates for the size of almost unavoidable sets of uniform length.
متن کاملUnavoidable patterns
Let Fk denote the family of 2-edge-colored complete graphs on 2k vertices in which one color forms either a clique of order k or two disjoint cliques of order k. Bollobás conjectured that for every 2 > 0 and positive integer k there is an n(k, 2) such that every 2-edge-coloring of the complete graph of order n ≥ n(k, 2) which has at least 2n2 ) edges in each color contains a member of Fk. This ...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 1987
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.3190110215