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June, 2021 Degree Bipartite Ramsey Numbers
Ye Wang, Yusheng Li, Yan Li
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Taiwanese J. Math. 25(3): 427-433 (June, 2021). DOI: 10.11650/tjm/201106

Abstract

Let $H \xrightarrow{s} G$ denote that any edge-coloring of $H$ by $s$ colors contains a monochromatic $G$. The degree Ramsey number $r_{\Delta}(G;s)$ is defined to be $\min \{ \Delta(H): H \xrightarrow{s} G \}$, and the degree bipartite Ramsey number $br_{\Delta}(G;s)$ is defined to be $\min \{ \Delta(H): H \xrightarrow{s} G \textrm{ and } \chi(H) = 2 \}$. In this note, we show that $r_{\Delta}(K_{m,n};s)$ is linear on $n$ with fixed $m$. We also evaluate $br_{\Delta}(G;s)$ for paths and other trees.

Funding Statement

This paper was supported in part by NSFC.

Acknowledgments

We are grateful to the editors and reviewers for their invaluable comments and suggestions which improve the manuscript greatly.

Citation

Download Citation

Ye Wang. Yusheng Li. Yan Li. "Degree Bipartite Ramsey Numbers." Taiwanese J. Math. 25 (3) 427 - 433, June, 2021. https://doi.org/10.11650/tjm/201106

Information

Received: 16 March 2020; Revised: 13 October 2020; Accepted: 25 November 2020; Published: June, 2021
First available in Project Euclid: 2 December 2020

Digital Object Identifier: 10.11650/tjm/201106

Subjects:
Primary: 05C55

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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Vol.25 • No. 3 • June, 2021
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