A Note on the Lower Bound for the Ramsey Number $R(7,9)$

Abstract

For integers $s,t\ge 1$, the Ramsey number $R(s,t)$ is defined to be the least positive integer $n$ such that every graph on $n$ vertices contains either a clique of order $s$ or an independent set of order $t$. In this note, the lower bound for the Ramsey number $R(7,9)$ is improved from $241$ to $242$. The new bound is obtained by searching the maximum common induced subgraph between two graphs with a depth variable local search technique.