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# The Multipartite Ramsey numbers $m_j(nK_2,C_7)$

@inproceedings{Rowshan2021TheMR,
title={The Multipartite Ramsey numbers \$m\_j(nK\_2,C\_7)\$},
author={Yaser Rowshan},
year={2021}
}
Assume that Kj×n be a complete, multipartite graph consisting of j partite sets and n vertices in each partite set. For given graphs G1 and G2, the multipartite Ramsey number (MR-number) mj(G1, G2) is the smallest integer t such that any subgraph G of the Kj×t, either G contains a copy of G1 or its complement relative to Kj×t contains a copy of G2. C. J. Jayawardene, E. T. Baskoro et al. (2016) gave the size of M-R-numbe mj(nK2, C7) for j ≥ 2 and n ≤ 6. Y. Rowshan et al. (2021) gave the size of… Expand
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The Multipartite Ramsey numbers $m_j(C_3, C_m, n_1K_2,n_2K_2,\ldots, n_iK_2)$
Assume that Kj×n be a complete, multipartite graph consisting of j partite sets and n vertices in each partite set. For given graphs G1, G2, . . . , Gn, the multipartite Ramsey number (M-R-number)Expand

#### References

SHOWING 1-10 OF 19 REFERENCES
The Size, Multipartite Ramsey Numbers for nK2 Versus Path–Path and Cycle
• Mathematics
• 2021
For given graphs G1,G2,…,Gn and any integer j, the size of the multipartite Ramsey number mj(G1,G2,…,Gn) is the smallest positive integer t such that any n-coloring of the edges of Kj×t contains aExpand
Set and size multipartite Ramsey numbers for stars
• Computer Science, Mathematics
• Discret. Appl. Math.
• 2018
The size multipartite Ramsey number for stars, denoted by m c, is the smallest positive integer s such that any k -coloring of the edges of K c × s contains a monochromatic copy of K 1, n i in color i for some i, 1 ≤ i ≤ k . Expand
On size multipartite Ramsey numbers for stars versus paths and cycles
• Computer Science, Mathematics
• Electron. J. Graph Theory Appl.
• 2017
The size tripartite Ramsey numbers of paths $P_n$ versus stars, with all $n\geq 2$ are investigated. Expand
On Size Multipartite Ramsey Numbers for Stars versus Cycles
• Computer Science
• ICGTIS
• 2015
The size multipartite Ramsey numbers mj ( G 1, G 2) is the smallest integer t such that every factorization of the graph Kj × t := F 1 ⊕ F 2 satisfies the following condition: either F 1 contains G 1 or F 2 contains G 2. Expand
Three-colour bipartite Ramsey number R_b(G_1, G_2, P_3)
• Physics, Computer Science
• Electron. J. Graph Theory Appl.
• 2020
This paper considers the three-colour bipartite Ramsey number R b ( G 1, G 2, P 3), and obtains the relations: R ( G, K 1, n ) ≤  R p ( G , K 1 , n +1 ) and R (G, H ) ≤ R b( G, H , P 3 ). Expand
The bipartite Ramsey numbers $BR(C_8, C_{2n})$
• Mathematics
• 2021
For given bipartite graphs G1, G2, . . . , Gt, the multicolor bipartite Ramsey number BR(G1, G2, . . . , Gt) is the smallest positive integer b such that any t-edge-coloring of Kb,b contains aExpand
Size multipartite Ramsey numbers for stripes versus small cycles
• Mathematics, Computer Science
• Electron. J. Graph Theory Appl.
• 2016
This paper obtains the exact values of the size Ramsey numbers $m_j(nK_2, C_m)$ for $j \ge 2$ and $m \in \{3,4,5,6\}$. Expand
Ramsey numbers in complete balanced multipartite graphs. Part I: Set numbers
• Computer Science
• Discret. Math.
• 2004
The de4nition of a multipartite Ramsey number is broadened still further, by incorporating o6-diagonal numbers, 4xing the number of vertices per partite set in the larger graph and then seeking the minimum number of such partite sets that would ensure the occurrence of certain speci4ed monochromatic multipartites subgraphs. Expand
Ramsey numbers in complete balanced multipartite graphs. Part II: Size numbers
• Computer Science, Mathematics
• Discret. Math.
• 2004
The definition of a multipartite Ramsey number is broadened still further, by incorporating off-diagonal numbers, fixing the number of vertices per partite set in the larger graph and then seeking the minimum number of such partite sets that would ensure the occurrence of certain specified monochromatic multipartites subgraphs. Expand
A proof of a conjecture on Ramsey numbers $B(2,2,3)$
• Mathematics
• 2021
The bipartite Ramsey number B(n1, n2, . . . , nt) is the least positive integer b such that, any coloring of the edges of Kb,b with t colors will result in a monochromatic copy of Kni,ni in the i−thExpand