کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4657502 1343742 2006 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A hypergraph extension of Turán's theorem
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
A hypergraph extension of Turán's theorem
چکیده انگلیسی

Fix l⩾r⩾2l⩾r⩾2. Let Hl+1(r) be the rr-uniform hypergraph obtained from the complete graph Kl+1Kl+1 by enlarging each edge with a set of r-2r-2 new vertices. Thus Hl+1(r) has (r-2)l+12+l+1 vertices and l+12 edges. We prove that the maximum number of edges in an nn-vertex rr-uniform hypergraph containing no copy of Hl+1(r) is(l)rlrnr+o(nr)as n→∞n→∞. This is the first infinite family of irreducible rr-uniform hypergraphs for each odd r>2r>2 whose Turán density is determined.Along the way, we give three proofs of a hypergraph generalization of Turán's theorem. We also prove a stability theorem for hypergraphs, analogous to the Simonovits stability theorem for complete graphs.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series B - Volume 96, Issue 1, January 2006, Pages 122–134
نویسندگان
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