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(2k−1)n. Here we conjecture that for any n≥m≥3 and k≥3,R(Pnk,Pmk)=R(Pnk,Cmk)=R(Cnk,Cmk)+1=(k−1)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 m≥3 and k≥4 the conjecture is equivalent to (only) the last equality for any 2m≥n≥m≥3. Finally we give a proof for the case m=3.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
