[vc_empty_space][vc_empty_space]
On Ramsey (4K2,P3)-minimal graphs
Wijaya K.a,b, Baskoro E.T.a, Assiyatun H.a, Suprijanto D.a
a Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB), Indonesia
b Department of Mathematics, Faculty of Mathematics and Natural Sciences, CGANT Research Group, University of Jember, 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]© 2017 Kalasalingam UniversityLet F,G, and H be simple graphs. We write F→(G,H) to mean that any red–blue coloring of all edges of F will contain either a red copy of G or a blue copy of H. A graph F (without isolated vertices) satisfying F→(G,H) and for each e∈E(F),(F−e)↛(G,H) is called a Ramsey (G,H)-minimal graph. The set of all Ramsey (G,H)-minimal graphs is denoted by ℛ(G,H). In this paper, we derive the necessary and sufficient condition of graphs belonging to ℛ(4K2,H), for any connected graph H. Moreover, we give a relation between Ramsey (4K2,P3)- and (3K2,P3)-minimal graphs, and Ramsey (4K2,P3)- and (2K2,P3)-minimal graphs. Furthermore, we determine all graphs in ℛ(4K2,P3).[/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]Edge coloring,Matching,Path,Ramsey minimal 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=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text]This research was supported by Research Grant “Program Penelitian Unggulan Perguruan Tinggi (PUPT)”, 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/10.1016/j.akcej.2017.08.003[/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]