TY - JOUR
T1 - Multicolour Ramsey numbers of paths and even cycles
AU - Davies, E.
AU - Jenssen, M.
AU - Roberts, B.
PY - 2017/6
Y1 - 2017/6
N2 - 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 Sárközy who showed that Rk(Cn)≤(k−(k/16k3+1))n+o(n). Here we show Rk(Cn)≤(k−¼)n+o(n), obtaining the first improvement to the coefficient of the linear term by an absolute constant.
AB - 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 Sárközy who showed that Rk(Cn)≤(k−(k/16k3+1))n+o(n). Here we show Rk(Cn)≤(k−¼)n+o(n), obtaining the first improvement to the coefficient of the linear term by an absolute constant.
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85016404137&partnerID=MN8TOARS
U2 - 10.1016/j.ejc.2017.03.002
DO - 10.1016/j.ejc.2017.03.002
M3 - Article
SN - 0195-6698
VL - 63
SP - 124
EP - 133
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
ER -