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Some infinite families of Ramsey (P3, Pn)-minimal trees
Rahmadani D.a, Baskoro E.T.a, Baca M.b, Assiyatun H.a, Semanicova-Fenovcikova A.b
a Combinatorial Mathematics Research Group, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB), Bandung, Indonesia
b Department of Applied Mathematics and Informatics, Technical University, Kosice, Slovakia
[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.For any given two graphs G and H, the notation F → (G, H) means that for any red-blue coloring of all the edges of F will create either a red subgraph isomorphic to G or a blue subgraph isomorphic to H. A graph F is a Ramsey (G, H)- minimal graph if F →(G, H) but F – e → (G, H), for every e ∈ E(F). The class of all Ramsey (G, H)-minimal graphs is denoted by R(G, H). In this paper, we construct some infinite families of trees belonging to R(P3, Pn), for n = 8 and 9. In particular, we give an algorithm to obtain an infinite family of trees belonging to R(P3, Pn), for n ≥ 10.[/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]Ramsey infinite,Ramsey minimal graph,Red-blue coloring,Subgraphs,Tree,Two-graphs[/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]Coloring,Ramsey infinite,Ramsey minimal graph,Tree[/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 Grants “Program Riset dan Inovasi KK ITB”, “Program Hibah PMDSU ITB-DIKTI”, 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/s12044-017-0361-4[/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]