کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4646708 | 1342310 | 2016 | 8 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Bounds on the number of edges in hypertrees
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
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چکیده انگلیسی
Let H be a k-uniform hypergraph. A chain in H is a sequence of its vertices such that every k consecutive vertices form an edge. In 1999 Katona and Kierstead suggested to use chains in hypergraphs as the generalization of paths. Although a number of results have been published on Hamiltonian chains in recent years, the generalization of trees with chains has still remained an open area. We generalize the concept of trees for uniform hypergraphs. We say that a k-uniform hypergraph H is a hypertree if every two vertices of H are connected by a chain, and an appropriate kind of cycle-free property holds. An edge-minimal hypertree is a hypertree whose edge set is minimal with respect to inclusion. After considering these definitions, we show that a k-uniform hypertree on n vertices has at least nâ(kâ1) edges if n>n0(k), and it has at most (nkâ1) edges. The latter bound is asymptotically sharp in 3-uniform case.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 339, Issue 7, 6 July 2016, Pages 1884-1891
Journal: Discrete Mathematics - Volume 339, Issue 7, 6 July 2016, Pages 1884-1891
نویسندگان
Gyula Y. Katona, Péter G.N. Szabó,