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On the ramsey numbers for the tree graphs versus certain generalised wheel graphs

Given two simple graphs G and H, the Ramsey number R(G, H) is the smallest integer n such that for any graph of order n, either it contains G or its complement contains H. Let T-n be a tree graph of order n and W-s,W-m be the generalised wheel graph K-s + C-m. In this paper, we show that for n >=...

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Main Authors: Chng, Zhi Yee, Tan, Ta Sheng, Wong, Kok Bin
Format: Article
Published: Elsevier 2021
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QA Mathematics
Online Access:http://eprints.um.edu.my/27184/
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spelling my.um.eprints.271842022-05-30T07:37:59Z http://eprints.um.edu.my/27184/ On the ramsey numbers for the tree graphs versus certain generalised wheel graphs Chng, Zhi Yee Tan, Ta Sheng Wong, Kok Bin QA Mathematics Given two simple graphs G and H, the Ramsey number R(G, H) is the smallest integer n such that for any graph of order n, either it contains G or its complement contains H. Let T-n be a tree graph of order n and W-s,W-m be the generalised wheel graph K-s + C-m. In this paper, we show that for n >= 5, s >= 2, R(T-n, W-s,W- 6) = (s + 1)(n - 1) + 1 and for n >= 5, s >= 1, R(T-n, W-s,W-7) = (s + 2)(n - 1) + 1. We also determine the exact value of R(T-n, W-s,W-m) for large nand s. (C) 2021 Elsevier B.V. All rights reserved. Elsevier 2021-08 Article PeerReviewed Chng, Zhi Yee and Tan, Ta Sheng and Wong, Kok Bin (2021) On the ramsey numbers for the tree graphs versus certain generalised wheel graphs. Discrete Mathematics, 344 (8). ISSN 0012-365X, DOI https://doi.org/10.1016/j.disc.2021.112440 <https://doi.org/10.1016/j.disc.2021.112440>. 10.1016/j.disc.2021.112440
institution Universiti Malaya
building UM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaya
content_source UM Research Repository
url_provider http://eprints.um.edu.my/
topic QA Mathematics
spellingShingle QA Mathematics
Chng, Zhi Yee
Tan, Ta Sheng
Wong, Kok Bin
On the ramsey numbers for the tree graphs versus certain generalised wheel graphs
description Given two simple graphs G and H, the Ramsey number R(G, H) is the smallest integer n such that for any graph of order n, either it contains G or its complement contains H. Let T-n be a tree graph of order n and W-s,W-m be the generalised wheel graph K-s + C-m. In this paper, we show that for n >= 5, s >= 2, R(T-n, W-s,W- 6) = (s + 1)(n - 1) + 1 and for n >= 5, s >= 1, R(T-n, W-s,W-7) = (s + 2)(n - 1) + 1. We also determine the exact value of R(T-n, W-s,W-m) for large nand s. (C) 2021 Elsevier B.V. All rights reserved.
format Article
author Chng, Zhi Yee
Tan, Ta Sheng
Wong, Kok Bin
author_facet Chng, Zhi Yee
Tan, Ta Sheng
Wong, Kok Bin
author_sort Chng, Zhi Yee
title On the ramsey numbers for the tree graphs versus certain generalised wheel graphs
title_short On the ramsey numbers for the tree graphs versus certain generalised wheel graphs
title_full On the ramsey numbers for the tree graphs versus certain generalised wheel graphs
title_fullStr On the ramsey numbers for the tree graphs versus certain generalised wheel graphs
title_full_unstemmed On the ramsey numbers for the tree graphs versus certain generalised wheel graphs
title_sort on the ramsey numbers for the tree graphs versus certain generalised wheel graphs
publisher Elsevier
publishDate 2021
url http://eprints.um.edu.my/27184/
_version_ 1735409509968379904
score 13.15806

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