Some results on the multipartite Ramsey numbers m(C3,C,n1K2,n2K2,…,nK2)

Rowshan, Yaser; Gholami, Mostafa; Shateyi, Stanford

doi:10.1016/j.heliyon.2022.e11431

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2023

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“…. , n i K 2 ) for j ≤ 6 and i, n i ≥ 1 and the size of M-R-number m 4 (C 3 , C 4 , nK 2 ) for n ≥ 1 have been computed in [17].…”

Section: Introductionmentioning

confidence: 99%

Multipartite Ramsey number of complete graphs versus matchings

Rowshan,

Gholami

2023

Art Discrete Appl. Math.

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Assume that K j×n is a complete and multipartite graph consisting of j partite sets and n vertices in each partite set. For the given graphs G 1 , G 2 , . . . , G n , the multipartite Ramsey number (M-R-number) m j (G 1 , G 2 , . . . , G n ), is the smallest integer t, such that for any nedge-coloring (G 1 , G 2 , . . . , G n ) of the edges of K j×t , G i contains a monochromatic copy of G i for at least one i. The size of M-R-number m j (nK 2 , C m ) for j, n ≥ 2 and 4 ≤ m ≤ 6, the size of M-R-number m j (nK 2 , C 7 ) for j ≥ 2 and n ≥ 2, the size of M-R-number m j (nK 2 , K 3 ) for each j, n ≥ 2, the size of M-R-number m j (K 3 , K 3 , n 1 K 2 , n 2 K 2 , . . . , n i K 2 ) for j ≤ 6 and i, n i ≥ 1, and the size of M-R-number m j (K 3 , K 3 , nK 2 ) for j ≥ 2 and n ≥ 1 have been computed in several previously published papers. In this article, we obtain the values of M-R-number m j (K m , nK 2 ) for j, n ≥ 2 and m ≥ 4.

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“…. , n i K 2 ) for j ≤ 6 and i, n i ≥ 1 and the size of M-R-number m 4 (C 3 , C 4 , nK 2 ) for n ≥ 1 have been computed in [17].…”

Section: Introductionmentioning

confidence: 99%