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arXiv · 2407.00872

Lower Bounds for Multicolor Star-Critical Ramsey Numbers

Mark Budden·Yash Shamsundar Khobragade·Siddhartha Sarkar
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Abstract

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 $5$.

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Mark Budden, Yash Shamsundar Khobragade, Siddhartha Sarkar. 2024-07-01. Lower Bounds for Multicolor Star-Critical Ramsey Numbers. https://arxiv.org/abs/2407.00872

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