منابع مشابه
An Ordered Turán Problem for Bipartite Graphs
Let F be a graph. A graph G is F -free if it does not contain F as a subgraph. The Turán number of F , written ex(n, F ), is the maximum number of edges in an F -free graph with n vertices. The determination of Turán numbers of bipartite graphs is a challenging and widely investigated problem. In this paper we introduce an ordered version of the Turán problem for bipartite graphs. Let G be a gr...
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Denote by I(G) the maximal number of independent points in a graph G and let or(G) = I(G), where G is the complement of G. Thus a(G) is the maximal p for which G contains a K, , a complete graph with p vertices. Denote byf(n, k, 1) the maximal m for which there is a graph with n points and m edges such that or(G) < k and I(G) < I. The function f(n, k, I) was introduced and investigated by Erdii...
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We consider an infinite version of the bipartite Turán problem. Let G be an infinite graph with V (G) = N, and let Gn be the n-vertex subgraph of G induced by the vertices {1, 2, . . . , n}. We show that if G is K2,t+1-free, then for infinitely many n, e(Gn) ≤ 0.471 √ tn3/2. Using the K2,t+1-free graphs constructed by Füredi, we construct an infinite K2,t+1-free graph with e(Gn) ≥ 0.23 √ tn3/2 ...
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of a thesis submitted to the Faculty of the Graduate School of Emory University in partial fulfillment of the requirements of the degree of Master of Science Department of Mathematics and Computer Science
متن کاملA Ramsey-type problem and the Turán numbers
For each n and k, we examine bounds on the largest number m so that for any k-coloring of the edges of Kn there exists a copy of Km whose edges receive at most k − 1 colors. We show that for k ≥ √ n+ Ω(n), the largest value of m is asymptotically equal to the Turán number t(n, b ( n 2 ) /kc), while for any constant > 0, if k ≤ (1 − ) √ n then the largest m is asymptotically larger than that Tur...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1979
ISSN: 0012-365X
DOI: 10.1016/0012-365x(79)90155-9