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Subdivision of graphs in R(mK2,P4)
Wijaya K.a, Baskoro E.T.b, Assiyatun H.b, Suprijanto D.b
a Graph, Combinatorics, and Algebra Research Group, Department of Mathematics, FMIPA, Universitas Jember, 68121, 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]© 2020 The Author(s)For any graphs F,G, and H, the notation F→(G,H) means that any red-blue coloring of all edges of F will contain either a red copy of G or a blue copy of H. The set R(G,H) consists of all Ramsey (G,H)-minimal graphs, namely all graphs F satisfying F→(G,H) but for each e∈E(F), (F−e)↛(G,H). In this paper, we propose a simple construction for creating new Ramsey minimal graphs from the previous known Ramsey minimal graphs (by subdivision operation). In particular, suppose F∈R(mK2,P4) and let e∈E(F) be an edge contained in a cycle of F, we construct a new Ramsey minimal graph in R((m+1)K2,P4) from graph F by subdividing the edge e four times.© 2020 The Author(s)Mathematics; Ramsey minimal graphs; Red-blue coloring; Matching; Path[/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]Matching,Mathematics,Path,Ramsey minimal graphs,Red-blue coloring[/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][{‘$’: ‘This research has been supported by the World Class Research (WCR) Program, Ministry of Research, Technology and Higher Education, Indonesia, Decree No. 7/E/KPT/2019 and Contract No. 127/SP2H/LT/DRPM/2019.The research of the first author has been supported by DRPM, Directorate General of Strengthening for Research and Development, Ministry of Research, Technology and Higher Education, Indonesia through ?Hibah Penelitian Dasar?, Decree No. 7/E/KPT/2019 and Contract No. 175/SP2H/LT/DRPM/2019.’}, {‘$’: ‘The research of the first author has been supported by DRPM, Directorate General of Strengthening for Research and Development, Ministry of Research, Technology and Higher Education , Indonesia through “Hibah Penelitian Dasar”, Decree No. 7/E/KPT/2019 and Contract No. 175/SP2H/LT/DRPM/2019 .’}, {‘$’: ‘This research has been supported by the World Class Research (WCR) Program, Ministry of Research, Technology and Higher Education , Indonesia, Decree No. 7/E/KPT/2019 and Contract No. 127/SP2H/LT/DRPM/2019 .’}][/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/10.1016/j.heliyon.2020.e03843[/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]