Multicolor, multipartite Ramsey numbers for quadrilateral
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913244790128640 |
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| author | Dybizbański, Janusz Rowshan, Yaser |
| author_facet | Dybizbański, Janusz Rowshan, Yaser |
| contents | The $p$-partite Ramsey number for quadrilateral, denoted by $r_p(C_4,k)$, is the least positive integer $n$ such that any coloring of the edges of a complete $p$-partite graph with $n$ vertices in each partition with $k$ colors will result in a monochromatic copy of $C_4$. In this paper, we present an upper bound for $r_p(C_4,k)$ and the exact values of $r_p(C_4,2)$ for all $p\geq2$. In tripartite case we show that $r_3(C_4,k) \leq \lfloor (k+1)^2/2\rfloor-1$ and the exact value of 4-color tripartite Ramsey number $r_3(C_4,4)=11$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_16816 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multicolor, multipartite Ramsey numbers for quadrilateral Dybizbański, Janusz Rowshan, Yaser Combinatorics The $p$-partite Ramsey number for quadrilateral, denoted by $r_p(C_4,k)$, is the least positive integer $n$ such that any coloring of the edges of a complete $p$-partite graph with $n$ vertices in each partition with $k$ colors will result in a monochromatic copy of $C_4$. In this paper, we present an upper bound for $r_p(C_4,k)$ and the exact values of $r_p(C_4,2)$ for all $p\geq2$. In tripartite case we show that $r_3(C_4,k) \leq \lfloor (k+1)^2/2\rfloor-1$ and the exact value of 4-color tripartite Ramsey number $r_3(C_4,4)=11$. |
| title | Multicolor, multipartite Ramsey numbers for quadrilateral |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2402.16816 |