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

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.

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Abstract

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.

Item Type: Article
Funders: UNSPECIFIED
Uncontrolled Keywords: Ramsey number; Tree; Generalised wheel graphs
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Institute of Mathematical Sciences
Depositing User: Ms Zaharah Ramly
Date Deposited: 30 May 2022 07:37
Last Modified: 30 May 2022 07:37
URI: http://eprints.um.edu.my/id/eprint/27184

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