Lower Bounds for Multicolor Star-Critical Ramsey Numbers
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911938766700544 |
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| author | Budden, Mark Khobragade, Yash Shamsundar Sarkar, Siddhartha |
| author_facet | Budden, Mark Khobragade, Yash Shamsundar Sarkar, Siddhartha |
| contents | 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 $5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00872 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lower Bounds for Multicolor Star-Critical Ramsey Numbers Budden, Mark Khobragade, Yash Shamsundar Sarkar, Siddhartha Combinatorics 05C55, 05D10 (Primary) 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 $5$. |
| title | Lower Bounds for Multicolor Star-Critical Ramsey Numbers |
| topic | Combinatorics 05C55, 05D10 (Primary) |
| url | https://arxiv.org/abs/2407.00872 |