Degree bipartite Ramsey numbers

2019/08/31 by Ye Wang, Wang, Ye, Yusheng Li +3
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1909.00147

openalex publication_date 2019/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H\xrightarrows G denote that any edge-coloring of H by s colors contains a monochromatic G. The degree Ramsey number r_Δ(G;s) is defined to be min\Δ(H):H\xrightarrows G\, and the degree bipartite Ramsey number br_Δ(G;s) is defined to be min\Δ(H):H\xrightarrows G and χ(H)=2\. In this note, we show that r_Δ(K_m,n;s) is linear on n with m fixed. We also determine br_Δ(G;s) where G are trees, including stars and paths, and complete bipartite graphs.

Related

• Degree Ramsey numbers for even cycles
• The bipartite Ramsey number br(C_2n, C_2m)
• Ramsey numbers of bounded degree trees versus general graphs
• Another view of Bipartite Ramsey numbers
• Recent developments in graph Ramsey theory