[vc_empty_space][vc_empty_space]
The Ramsey Number for Tree Versus Wheel with Odd Order
Hafidh Y.a, Baskoro E.T.a
a Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, 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]© 2021, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.Chen et al. (Appl Math Lett 17:281–285, 2004) conjectured that for even m, R(Tn, Wm) = 2 n- 1 if the maximum degree Δ(Tn) is small. However, they did not state how small it is. Related to this conjecture, it is also interesting to know which tree Tn causes the Ramsey number R(Tn, Wm) to be greater than 2 n- 1 whenever m is even. In this paper, we determine the Ramsey number R(Tn, W8) for all trees Tn with Δ(Tn) ≥ n- 3. For most cases of these trees, R(Tn, W8) > 2 n- 1. Furthermore, we also prove that for certain values of n, the Ramsey number R(Tn, Wm) is greater than 2 n- 1 if Δ(Tn) ≥ n- 3 and m is even. Finally, we refine the above conjecture by giving an upper bound on the maximum degree of the tree Tn.[/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]Ramsey number,Tree,Wheel[/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]We would like to thank the referees for their valuable remarks and suggestions which greatly helped to improve this article. This research has been supported by the World Class Research (WCR) Program, Ministry of Research and Technology/National Research and Innovation Agency, 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/s40840-020-01055-x[/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]