Translator Disclaimer
2021 Degree Bipartite Ramsey Numbers
Ye Wang, Yusheng Li, Yan Li
Taiwanese J. Math. Advance Publication 1-7 (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.

Citation

Download Citation

Ye Wang. Yusheng Li. Yan Li. "Degree Bipartite Ramsey Numbers." Taiwanese J. Math. Advance Publication 1 - 7, 2021. https://doi.org/10.11650/tjm/201106

Information

Published: 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

JOURNAL ARTICLE
7 PAGES


SHARE
Advance Publication
Back to Top