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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.02641 |
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Table of Contents:
- For graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the smallest $r$ such that any red-blue edge coloring of $K_r$ contains a red $G$ or a blue $H$. The path-critical Ramsey number $R_π(G,H)$ is the largest $n$ such that any red-blue edge coloring of $K_r \setminus P_{n}$ contains a red $G$ or a blue $H$, where $r=R(G,H)$ and $P_{n}$ is a path of order $n$. In this note, we show a general upper bound for $R_π(G,H)$, and determine the exact values for some cases of $R_π(G,H)$.