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Some unicyclic Ramsey (P 3, P n)-minimal graphs
Rahmadani D.a, Baskoro E.T.a, Tri E.a
a Combinatorial Mathematics Research Group Faculty of Mathematics, Natural Sciences Institut Teknologi Bandung (ITB), 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]© Published under licence by IOP Publishing Ltd.Let F, G and H be graphs. We write F → (G, H) if whenever every edge of F is colored by red or blue, then F will contain either a red copy of G or a blue copy of H. The graph F is called Ramsey (G, H)-minimal graph if F → (G, H) and F – e (G, H) for every e E(F). The class of all Ramsey (G, H)-minimal graphs (up to isomorphism) is denoted by (G, H). In this paper, we give explicitly an infinite family of unicyclic graphs in, (P 3, Pn ), for n = 6 and 7 constructed from trees in the same class. Moreover, we give a method to construct the unicyclic graphs in (P 3, P n+2) from existing unicyclic graphs in (P 3, P n), for each n ≥ 6.[/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]Unicyclic,Unicyclic graph[/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 research grant ”Program Riset dan Inovasi KK-Institut Teknologi Bandung 2018”.[/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/10.1088/1742-6596/1127/1/012062[/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]