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On size multipartite ramsey numbers of mK1,n VERSUS P3 OR K 1,3
Lusiani A.a, Baskoro E.T.b, Saputro S.W.b
a Politeknik Neceri Bandung, Bandung, 40012, Indonesia
b Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, 40132, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 2019 Jangjeon Research Institute for Mathematical Sciences and Physics. All rights reserved.For given two simple graphs G and H. the size multipartite Ramsey number mj(G, H), is the smallest natural number t such that every 2-edge coloring on the edges of the complete balanced multipartite graph K3xt has a monochromatic copy of G in the first color or H in the second color. Hattingh and Henning (1998) gave the results for the size bipartite Ramsey numbers of stars versus paths, m-2 (K1 .m, Pn), for m, n > 2. In 2016, we have derived the size tripartite Ramsey numbers m3(mK1,,P3), for m > 1 ,n > 2, where mK1,n is a disjoint union of m copies of a star A’i,n and P3 is a path of order 3. In this paper, we determine the size multipartite Ramsey numbers mj(mK\,n, Fx) and mj(mK1,n K1,3), for all integers m,n > 2 and j > 3. We also provide an exact value of m2(m/ 2 and m3(mK1,.K 1,3),for (m = 1, n > 1) or (n = 1,m > 1).[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Path,Size multipartite ramsey number,Star[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.17777/pjms2019.22.1.59[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]