Ramsey numbers of paths and graphs of the same order

Chaoping Pei, Yusheng Li

For graphs $F_n$ and $G_n$ of order $n$, if $R(F_n,G_n)=(\chi (G_n)-1)(n-1)+\sigma (G_n)$, then $F_n$ is said to be $G_n$-good, where $\sigma (G_n)$ is the minimum size of a color class among all…