منابع مشابه
The Density Turán Problem
Let H be a graph on n vertices and let the blow-up graph G[H] be defined as follows. We replace each vertex vi of H by a cluster Ai and connect some pairs of vertices of Ai and Aj if (vi, vj) was an edge of the graph H. As usual, we define the edge density between Ai and Aj as d(Ai, Aj) = e(Ai, Aj) |Ai||Aj | . We study the following problem. Given densities γij for each edge (i, j) ∈ E(H). Then...
متن کاملRainbow Turán Problems
For a fixed graph H, we define the rainbow Turán number ex∗(n,H) to be the maximum number of edges in a graph on n vertices that has a proper edge-colouring with no rainbow H. Recall that the (ordinary) Turán number ex(n,H) is the maximum number of edges in a graph on n vertices that does not contain a copy of H. For any non-bipartite H we show that ex∗(n,H) = (1+o(1))ex(n,H), and if H is colou...
متن کاملOn two Turán Numbers
Let Hð3;1Þ denote the complete bipartite graph K3;3 with an edge deleted. For given graphs G and F , the Turán numbers exðG; FÞ denote the maximum number of edges in a subgraph of G containing no copy of F . We prove that exðKn;n;Hð3; 1ÞÞ ð4= ffiffiffi 7 p n þOðnÞ 1:5119n þOðnÞ and that exðKn;Hð3; 1ÞÞ ð1=5Þ ffiffiffiffiffi 15 p n þOðnÞ 0:7746n þ OðnÞ, which improve earlier results of Mubayi-Wes...
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 کاملℓ-Degree Turán Density
Access to the published version may require subscription. Abstract. Let Hn be a k-graph on n vertices. For 0 ≤ ℓ < k and an ℓ-subset T of V (Hn), define the degree deg(T) of T to be the number of (k − ℓ)-subsets S such that S ∪ T is an edge in Hn. Let the minimum ℓ-degree of Hn be δ ℓ (Hn) = min{deg(T) : T ⊆ V (Hn) and |T | = ℓ}. Given a family F of k-graphs, the ℓ-degree Turán number ex ℓ (n, ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2018
ISSN: 1077-8926
DOI: 10.37236/6555