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The Size, Multipartite Ramsey Numbers for nK 2 Versus Path–Path and Cycle

Author

Listed:
  • Yaser Rowshan

    (Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 66731-45137, Iran)

  • Mostafa Gholami

    (Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 66731-45137, Iran)

  • Stanford Shateyi

    (Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa)

Abstract

For given graphs G 1 , G 2 , … , G n and any integer j , the size of the multipartite Ramsey number m j ( G 1 , G 2 , … , G n ) is the smallest positive integer t such that any n -coloring of the edges of K j × t contains a monochromatic copy of G i in color i for some i , 1 ≤ i ≤ n , where K j × t denotes the complete multipartite graph having j classes with t vertices per each class. In this paper, we computed the size of the multipartite Ramsey numbers m j ( K 1 , 2 , P 4 , n K 2 ) for any j , n ≥ 2 and m j ( n K 2 , C 7 ) , for any j ≤ 4 and n ≥ 2 .

Suggested Citation

  • Yaser Rowshan & Mostafa Gholami & Stanford Shateyi, 2021. "The Size, Multipartite Ramsey Numbers for nK 2 Versus Path–Path and Cycle," Mathematics, MDPI, vol. 9(7), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:764-:d:528507
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