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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.
Budden et al. (Sun,) studied this question.
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