منابع مشابه
More Turán-Type Theorems for Triangles in Convex Point Sets
We study the following family of problems: Given a set of n points in convex position, what is the maximum number triangles one can create having these points as vertices while avoiding certain sets of forbidden configurations. As forbidden configurations we consider all 8 ways in which a pair of triangles in such a point set can interact. This leads to 256 extremal Turán-type questions. We giv...
متن کاملThe Turán Number Of The Fano Plane
Moreover, the only extremal configuration can be obtained by partitioning an n-element set into two almost equal parts, and taking all the triples that intersect both of them. This extends an earlier result of de Caen and Füredi, and proves an old conjecture of V. Sós. In addition, we also prove a stability result for the Fano plane, which says that a 3-uniform hypergraph with density close to ...
متن کاملThe Turán number of sparse spanning graphs
For a graph H, the extremal number ex(n,H) is the maximum number of edges in a graph of order n not containing a subgraph isomorphic to H. Let δ(H) > 0 and ∆(H) denote the minimum degree and maximum degree of H, respectively. We prove that for all n sufficiently large, if H is any graph of order n with ∆(H) ≤ √ n/200, then ex(n,H) = ( n−1 2 ) +δ(H)−1. The condition on the maximum degree is tigh...
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...
متن کاملOn the Turán Number of Triple Systems
For a family of r-graphs F , the Turán number ex(n,F) is the maximum number of edges in an n vertex r-graph that does not contain any member of F . The Turán density π(F) = lim n→∞ ex(n,F) ( n r ) . When F is an r-graph, π(F) 6= 0, and r > 2, determining π(F) is a notoriously hard problem, even for very simple r-graphs F . For example, when r = 3, the value of π(F) is known for very few (< 10) ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2017
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2016.09.003