کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5776864 | 1413644 | 2017 | 6 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A note on fractional disjoint transversals in hypergraphs
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
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چکیده انگلیسی
A transversal in a hypergraph H is a subset of vertices that has a nonempty intersection with every edge of H. A transversal family F of H is a family of (not necessarily distinct) transversals of H. The effective transversal-ratio of the family F is the ratio of the number of sets in F over the maximum times rF any element appears in F. The fractional disjoint transversal number FDT(H) is the supremum of the effective transversal-ratio taken over all transversal families. That is, FDT(H)=supF|F|ârF. Using a connection with not-all-equal 3-SAT, we prove that if H is a 3-regular 3-uniform hypergraph, then FDT(H)â¥2, which proves a known conjecture. Using probabilistic arguments, we prove that for all kâ¥3, if H is a k-regular k-uniform hypergraph, then FDT(H)â¥1â(1â(kâ1k)1k1kâ1), and that this bound is essentially best possible.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 340, Issue 10, October 2017, Pages 2349-2354
Journal: Discrete Mathematics - Volume 340, Issue 10, October 2017, Pages 2349-2354
نویسندگان
Michael A. Henning, Anders Yeo,