The generalized Ramsey number r(Kn,n, C2k, 3)

Authors

• Patrick Bennett, Western Michigan University

Document Type

Lecture

Publication Date

2-18-2026

Abstract

The generalized Ramsey number r(G, H, q) is the minimum number of colors needed to edge-color the graph G so that every subgraph isomorphic to H receives at least q colors. In this talk we discuss

r(K_n,n, C_2k, 3). For the case k = 2, this Ramsey number was determined to be asymptotically 2n/3 by Axenovich, Furedi and Mubayi (lower bound) and Joos and Mubayi (upper bound). We prove new upper and lower bounds for all k ≥ 3, and determine r(K_n,n, C₆, 3) asymptotically. This talk is about joint work with Deepak Bal.

Relational Format

presentation

Recommended Citation

Bennett, Patrick, "The generalized Ramsey number r(Kn,n, C2k, 3)" (2026). Combinatorics Seminar. 128.
https://egrove.olemiss.edu/math_combinatorics/128

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