  The star-critical Ramsey number is a refinement of the concept of a Ramsey
number. In this paper, we give equivalent criteria for which the star-critical
Ramsey number vanishes. Next, we provide a new general lower bound for
multicolor star-critical Ramsey numbers whenever it does not vanish. As an
application, we evaluate $r_*(P_k, P_3, P_3)$, where $P_n$ is a path of order
$n$. In the process of proving these results, we also show that $r_*(C_5,
P_3)=3$, where $C_5$ is a cycle of order $5$.
