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Connected size Ramsey number for matchings vs. small stars or cycles
Rahadjeng B.a, Baskoro E.T.a, Assiyatun H.a
a Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB), Bandung, 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]© Indian Academy of Sciences.The notation F → (G, H) means that if the edges of F are colored red and blue, then the red subgraph contains a copy of G or the blue subgraph contains a copy of H. The connected size Ramsey number rc(G, H) of graphs G and H is the minimum size of a connected graph F satisfying F → (G, H). For m ≥ 2, the graph consisting of m independent edges is called a matching and is denoted by mK2. In 1981, Erdös and Faudree determined the size Ramsey numbers for the pair (mK2, K1,t). They showed that the disconnected graph mK1,t → (mK2, K1,t) for t,m ≥ 1. In this paper, we will determine the connected size Ramsey number rc(nK2, K1,3) for n ≥ 2 and rc(3K2,C4). We also derive an upper bound of the connected size Ramsey number rc(nK2,C4), for n ≥ 4.[/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,Cycle,Disconnected graph,Independent edges,Matching,Matchings,Size-Ramsey number,Upper Bound[/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]Connected size ramsey number,Cycle,Matching,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]This research was supported by Research Grant “Program Riset dan Inovasi KK-ITB”, 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/10.1007/s12044-017-0366-z[/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]