Computation of the Ramsey numbers \(R(C_4,K_9)\) and \(R(C_4,K_{10})\) (Q2829342)

The cycle-complete Ramsey number \(R(C_n, K_m)\) is the minimal natural number \(N\) such that, for any (red/blue)-coloring of the edges of the complete graph \(K_N\), there is either red copy of the cycle \(C_n\) or blue copy of \(K_m\).NEWLINENEWLINEThe author's computer obtained: NEWLINE\[NEWLINER(C_4, K_g)=30,\quad R(C_4,K_{10})=36,NEWLINE\]NEWLINE NEWLINE\[NEWLINE39\leq R(C_4,K_{11})\leq 44,\quad 42\leq R(C_4, K_{12})\leq 52.NEWLINE\]NEWLINE Some speculative remarks after the references must ensure the reader to trust in the computer.NEWLINENEWLINEFor recent hand-made progress in computation of \(R(K_2^n,K_m)\) see [\textit{G. Fiz Pontiveros} et al., J. Lond. Math. Soc., II. Ser. 89, No. 3, 680--702 (2014; Zbl 1295.05253)].