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The Ramsey numbers for disjoint unions of graphs
Hasmawatia, Baskoro E.T.a, Assiyatun H.a
a Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB), 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]For given graphs G and H, the Ramsey number R (G, H) is the smallest natural number n such that for every graph F of order n: either F contains G or the complement of F contains H . In this paper we investigate the Ramsey number of a disjoint union of graphs R ({n-ary union}i = 1k Gi, H). For any natural integer k, we contain a general upper bound, R (kG, H) ≤ R (G, H) + (k – 1) | V (G) |. We also show that if m = 2 n – 4, 2 n – 8 or 2 n – 6, then R (kSn, Wm) = R (Sn, Wm) + (k – 1) n. Furthermore, if | Gi | > (| Gi | – | Gi + 1 |) (χ (H) – 1) and R (Gi, H) = (χ (H) – 1) (| Gi | – 1) + 1, for each i, then R ({n-ary union}i = 1k Gi, H) = R (Gk, H) + ∑i = 1k – 1 | Gi |. © 2007 Elsevier B.V. All rights reserved.[/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]Disjoint unions,Ramsey number[/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]Disjoint union of graphs,Graph,Ramsey number[/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][/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.disc.2007.04.026[/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]