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Restricted Size Ramsey Number for 2K2 versus Dense Connected Graphs of Order Six
Silaban D.R.a,b, Baskoro E.T.a, Uttunggadewa S.a
a Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, 40132, Indonesia
b Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, 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]© Published under licence by IOP Publishing Ltd.Let G and H be simple graphs. The Ramsey number r(G, H) for a pair of graphs G and H is the smallest number r such that any red-blue coloring of the edges of Kr contains a red subgraph G or a blue subgraph H. The size Ramsey number for a pair of graphs G and H is the smallest number such that there exists a graph F with size satisfying the property that any red-blue coloring of the edges of F contains a red subgraph G or a blue subgraph H. Additionally, if the order of F in the size Ramsey number equals r(G, H), then it is called the restricted size Ramsey number. In 1972, Chvátal and Harary gave the Ramsey number for 2K 2 versus any graph H with no isolates. In 1983, Harary and Miller started the investigation of the (restricted) size Ramsey number for some pairs of small graphs with order at most four. In 1983, Faudree and Sheehan continued the investigation and summarized the complete results on the (restricted) size Ramsey number for all pairs of small graphs with order at most four. In 1998, Lortz and Mengenser gave both the size Ramsey number and the restricted size Ramsey number for all pairs of small forests with order at most five. Lately, we investigate the restricted size Ramsey number for 2K 2 versus all connected graphs of order five. In this work, we continue the investigation on the restricted size Ramsey number for a pair of small graphs. In particularly, for 2K 2 versus dense connected graph of order six.[/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]Connected graph,Ramsey numbers,Red-blue coloring,Size-Ramsey number,Subgraphs[/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][/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]This research was supported by the Research Grant ”Program Penelitian Unggulan Perguruan Tinggi” and ”Penelitian Disertasi Doktor 2017” Ministry of Research, Technology, and Higher Education, Indonesia.[/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/10.1088/1742-6596/1008/1/012034[/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]