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

Yaser Rowshan, Mostafa Gholami and Stanford Shateyi
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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

Mathematics, 2021, vol. 9, issue 7, 1-12

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 .

Keywords: Ramsey numbers; multipartite Ramsey numbers; stripes; paths; cycle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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