Generalized Ramsey numbers of cycles, paths, and hypergraphs

Authors

• Deepak Bal, Montclair State UniversityFollow
• Patrick Bennett, Western Michigan University
• Emily Heath, California State Polytechnic University, Pomona
• Shira Zerbib, Iowa State University

Document Type

Article

Publication Date

2-1-2026

Journal / Book Title

European Journal of Combinatorics

Abstract

Given a k -uniform hypergraph G and a set of k -uniform hypergraphs H , the generalized Ramsey number f ( G , H , q ) is the minimum number of colors needed to edge-color G so that every copy of every hypergraph H ∈ H in G receives at least q different colors. In this note we obtain bounds, some asymptotically sharp, on several generalized Ramsey numbers, when G = K n or G = K n , n and H is a set of cycles or paths, and when G = K n k and H contains a clique on k + 2 vertices or a tight cycle.

DOI

10.1016/j.ejc.2025.104281

MSU Digital Commons Citation

Bal, Deepak; Bennett, Patrick; Heath, Emily; and Zerbib, Shira, "Generalized Ramsey numbers of cycles, paths, and hypergraphs" (2026). Department of Mathematics Faculty Scholarship and Creative Works. 227.
https://digitalcommons.montclair.edu/mathsci-facpubs/227

Rights

This article is distributed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International license.