Multicolour Ramsey numbers of paths and even cycles
Abstract
We prove new upper bounds on the multicolour Ramsey numbers of paths and even cycles. It is well known that (k-1)n+o(n)≤ Rk(Pn)≤ Rk(Cn)≤ kn+o(n). The upper bound was recently improved by S\'ark\"ozy who showed that Rk(Cn)≤(k-k16k3+1)n+o(n). Here we show Rk(Cn) ≤ (k-14)n +o(n), obtaining the first improvement to the coefficient of the linear term by an absolute constant.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.