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An extremal problem in graph theory
Israel Journal of Mathematics, 1968It is proved that the maximum number of cut-vertices in a connected graph withn vertices andm edges is $$max\left\{ {q:m \leqq (_2^{n - q} ) + q} \right\}$$ All the extremal graphs are determined and the corresponding problem for cut-edges is also solved.
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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.
Paul Erdos
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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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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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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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AN EXTREMAL PROBLEM IN GRAPH THEORY
The Quarterly Journal of Mathematics, 1980Abbott, H. L., Hanson, D., Liu, A. C.
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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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