کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5776822 | 1413642 | 2017 | 9 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Ramsey numbers of uniform loose paths and cycles
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
Recently, determining the Ramsey numbers of loose paths and cycles in uniform hypergraphs has received considerable attention. It has been shown that the 2-color Ramsey number of a k-uniform loose cycle Cnk, R(Cnk,Cnk), is asymptotically 12(2kâ1)n. Here we conjecture that for any nâ¥mâ¥3 and kâ¥3,R(Pnk,Pmk)=R(Pnk,Cmk)=R(Cnk,Cmk)+1=(kâ1)n+m+12.Recently the case k=3 was proved by the authors. In this paper, first we show that this conjecture is true for k=3 with a much shorter proof. Then, we show that for fixed mâ¥3 and kâ¥4 the conjecture is equivalent to (only) the last equality for any 2mâ¥nâ¥mâ¥3. Finally we give a proof for the case m=3.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 340, Issue 6, June 2017, Pages 1426-1434
Journal: Discrete Mathematics - Volume 340, Issue 6, June 2017, Pages 1426-1434
نویسندگان
G.R. Omidi, M. Shahsiah,