Lower Bounds for Multicolor Star-Critical Ramsey Numbers

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_*(Pₖ, P₃, P₃), where Pₙ is a path of order n. In the process of proving these results, we also show that r_*(C₅, P₃)=3, where C₅ is a cycle of order $5$.