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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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 |
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QA Mathematics Chng, Zhi Yee Tan, Ta Sheng Wong, Kok Bin On the ramsey numbers for the tree graphs versus certain generalised wheel graphs |
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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 |
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http://eprints.um.edu.my/27184/ |
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1735409509968379904 |