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
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,