Local Ramsey numbers for copies of cycles Original Research Article

We prove that the 2-local Ramsey number R2-loc(nC4) is equal to R(nC4). Moreover, R2-loc(nC2k+1)=n(4k+3)−2 for k⩾2 or n⩾2 and R2-loc(k(C3∪C4))=15k−2 for k⩾1.