  Given a pair of graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the
smallest $N$ such that every red-blue coloring of the edges of the complete
graph $K_N$ contains a red copy of $G$ or a blue copy of $H$. If graph $G$ is
connected, it is well known and easy to show that $R(G,H) \geq
(|G|-1)(\chi(H)-1)+\sigma(H)$, where $\chi(H)$ is the chromatic number of $H$
and $\sigma$ the size of the smallest color class in a $\chi(H)$-coloring of
$H$. A graph $G$ is called $H$-good if $R(G,H)= (|G|-1)(\chi(H)-1)+\sigma(H)$.
The notion of Ramsey goodness was introduced by Burr and Erd\H{o}s in 1983 and
has been extensively studied since then. In this short note we prove that
$n$-vertex path $P_n$ is $H$-good for all $n\geq 4|H|$. This proves in a strong
form a conjecture of Allen, Brightwell, and Skokan.
