Turán - type Problems in Extremal Combinatorics Adam Marcus
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چکیده
منابع مشابه
Symmetry in Turán Sums of Squares Polynomials from Flag Algebras
Turán problems in extremal combinatorics concern asymptotic bounds on the edge densities of graphs and hypergraphs that avoid specified subgraphs. The theory of flag algebras proposed by Razborov provides powerful semidefinite programming based methods to find sums of squares that establish edge density inequalities in Turán problems. Working with polynomial analogs of the flag algebra entities...
متن کاملExtremal Results in Random Graphs
According to Paul Erdős [Some notes on Turán’s mathematical work, J. Approx. Theory 29 (1980), page 4] it was Paul Turán who “created the area of extremal problems in graph theory”. However, without a doubt, Paul Erdős popularized extremal combinatorics, by his many contributions to the field, his numerous questions and conjectures, and his influence on discrete mathematicians in Hungary and al...
متن کاملDaisies and Other Turán Problems
Our aim in this note is to make some conjectures about extremal densities of daisy-free families, where a ‘daisy’ is a certain hypergraph. These questions turn out to be related to some Turán problems in the hypercube, but they are also natural in their own right. We start by giving the daisy conjectures, and some related problems, and shall then go on to describe the connection with vertex-Tur...
متن کاملTriple Systems Not Containing a Fano Configuration
Given a 3-uniform hypergraph F , let ex3(n,F) denote the maximum possible size of a 3-uniform hypergraph of order n that does not contain any subhypergraph isomorphic to F . Our terminology follows that of [16] and [10], which are comprehensive survey articles of Turán-type extremal graph and hypergraph problems, respectively. Also see the monograph of Bollobás [2]. There is an extensive litera...
متن کاملOn the Turán Number of Forests
The Turán number of a graph H, ex(n,H), is the maximum number of edges in a graph on n vertices which does not have H as a subgraph. We determine the Turán number and find the unique extremal graph for forests consisting of paths when n is sufficiently large. This generalizes a result of Bushaw and Kettle [Combinatorics, Probability and Computing 20:837–853, 2011]. We also determine the Turán n...
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تاریخ انتشار 2009