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On the restricted size Ramsey number involving a path P 3
Silaban D.R.a,b, Baskoro E.T.a, Uttunggadewa S.a
a Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, 40132, Indonesia
b Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas, 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]© 2019 Sciendo. All rights reserved. For any pair of graphs G and H, both the size Ramsey number r(G, H) and the restricted size Ramsey number r ∗ (G, H) are bounded above by the size of the complete graph with order equals to the Ramsey number r(G, H), and bounded below by e(G) + e(H) − 1. Moreover, trivially, r(G, H) ≤ r ∗ (G, H). When introducing the size Ramsey number for graph, Erdös et al. (1978) asked two questions; (1) Do there exist graphs G and H such that r(G, H) attains the upper bound? and (2) Do there exist graphs G and H such that r(G, H) is significantly less than the upper bound? In this paper we consider the restricted size Ramsey number r ∗ (G, H). We answer both questions above for r ∗ (G, H) when G = P 3 and H is a connected 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=”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]Connected graph,Path,Restricted size ramsey number,Star[/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]The authors would like to thank the referees for their careful reading of the manuscript and valuable suggestions. This research was supported by the Research Grant ”Penelitian Dasar Unggulan Perguruan Tinggi”, 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/10.7151/dmgt.2188[/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]