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Extremal problems in graph theory
Journal of Graph Theory, 1977AbstractThe aim of this note is to give an account of some recent results and state a number of conjectures concerning extremal properties of graphs.
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2005
In this chapter we study how global parameters of a graph, such as its edge density or chromatic number, can influence its local substructures. How many edges, for instance, do we have to give a graph on n vertices to be sure that, no matter how these edges are arranged, the graph will contain a K r subgraph for some given r?
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In this chapter we study how global parameters of a graph, such as its edge density or chromatic number, can influence its local substructures. How many edges, for instance, do we have to give a graph on n vertices to be sure that, no matter how these edges are arranged, the graph will contain a K r subgraph for some given r?
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On an extremal inverse problem in graph theory
Journal of Applied and Industrial Mathematics, 2015Summary: We consider the problem of constructing a graph having some given number of independent sets. The bounds are obtained for the number of vertices in bipartite graphs with the prescribed number of independent sets and for the number of inclusion maximal independent sets.
Daĭnyak, A. B., Kurnosov, A. D.
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Finite Geometry and Extremal Graph Theory
2022The present paper reviews some results about the Turan number of bipartite graphs and about clique-free pseudorandom graphs. The geometric aspect of known construction is highlighted, sometimes providing a different proof of known results and giving a new prospective on how to tackles such problems. Some new results are also presented.
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AN EXTREMAL PROBLEM IN GRAPH THEORY
The Quarterly Journal of Mathematics, 1980Abbott, H. L., Hanson, D., Liu, A. C.
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On some extremal problems in graph theory
Israel Journal of Mathematics, 1965Der Verf. beweist, daß für eine genügend große Konstante \(c\) jeder Graph \(G\) mit \(n\) Punkten und \(cn^{3/2}\) Kanten ein Sechseck \(x_1,x_2,x_3,x_4,x_5,x_6\) enthält und dazu noch einen siebenten Punkt \(y\), der mit \(x_1,x_3\) und \(x_5\) verbunden ist.
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Extremal Combinatorics in Geometry and Graph Theory
2013We study a problem in extremal geometry posed by Paul Erdos and George Szekeres in 1935. This problem is to find the smallest positive integer N(n) such that every point set in general position (no three on a line) of N(n) points contains the vertex set of a convex n-gon.
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Results in Extremal Graph and Hypergraph Theory
2011In graph theory, as in many fields of mathematics, one is often interested in finding the maxima or minima of certain functions and identifying the points of optimality. We consider a variety of functions on graphs and hypegraphs and determine the structures that optimize them.
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