Ramsey numbers of connected 4-clique matchings
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910870625320960 |
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| author | Kanopthamakun, Krit Vichitkunakorn, Panupong |
| author_facet | Kanopthamakun, Krit Vichitkunakorn, Panupong |
| contents | In this paper, we determine the exact value of the $2$-edge-coloring Ramsey number of a connected $4$-clique matching $c(nK_4)$, which is a set of connected graphs containing an $nK_4$ is $13n-3$ for any positive integer $n \geq 3$. This is an extension of the result by Roberts (2017), which is proved only for $n\geq 18$. We also show that the result still holds when $n=2$ provided that $R_2(2K_4) \leq 23$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_08412 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ramsey numbers of connected 4-clique matchings Kanopthamakun, Krit Vichitkunakorn, Panupong Combinatorics Discrete Mathematics 05C15, 05D10 In this paper, we determine the exact value of the $2$-edge-coloring Ramsey number of a connected $4$-clique matching $c(nK_4)$, which is a set of connected graphs containing an $nK_4$ is $13n-3$ for any positive integer $n \geq 3$. This is an extension of the result by Roberts (2017), which is proved only for $n\geq 18$. We also show that the result still holds when $n=2$ provided that $R_2(2K_4) \leq 23$. |
| title | Ramsey numbers of connected 4-clique matchings |
| topic | Combinatorics Discrete Mathematics 05C15, 05D10 |
| url | https://arxiv.org/abs/2306.08412 |