Vertex Turán problems in the hypercube
نویسندگان
چکیده
منابع مشابه
Vertex Turán problems in the hypercube
Let Qn be the n-dimensional hypercube: the graph with vertex set {0, 1} and edges between vertices that differ in exactly one coordinate. For 1 ≤ d ≤ n and F ⊆ {0, 1} we say that S ⊆ {0, 1} is F -free if every embedding i : {0, 1} → {0, 1} satisfies i(F ) 6⊆ S. We consider the question of how large S ⊆ {0, 1} can be if it is F -free. In particular we generalise the main prior result in this are...
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For any graphsH,G, define ex(H,G) (ex0(H,G)) to be the maximum number of edges (vertices) which may be contained in a subgraph (induced subgraph) H ′ of H without H ′ containing G as a subgraph. The study of these quantities for various choices of H and G are known as Turán type problems. We are interested in the quantities ex(Qn, G) and ex (Qn, G), where Qn denotes the n-dimensional hypercube....
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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...
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For an l-graph G, the Turán number ex(n,G) is the maximum number of edges in an n-vertex l-graph H containing no copy of G. The limit π(G) = limn→∞ ex (n,G)/ ( n l ) is known to exist [8]. The Ramsey-Turán density ρ(G) is defined similarly to π(G) except that we restrict to only those H with independence number o(n). A result of Erdős and Sós [3] states that π(G) = ρ(G) as long as for every edg...
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We consider an infinite version of the bipartite Turán problem. Let G be an infinite graph with V (G) = N, and let Gn be the n-vertex subgraph of G induced by the vertices {1, 2, . . . , n}. We show that if G is K2,t+1-free, then for infinitely many n, e(Gn) ≤ 0.471 √ tn3/2. Using the K2,t+1-free graphs constructed by Füredi, we construct an infinite K2,t+1-free graph with e(Gn) ≥ 0.23 √ tn3/2 ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2010
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2009.07.004