Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776822 | Discrete Mathematics | 2017 | 9 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
G.R. Omidi, M. Shahsiah,