On the set-coloring Ramsey numbers of graphs
Mengya He, Yaping Mao

TL;DR
This paper investigates set-coloring Ramsey numbers for various graphs, providing exact values, bounds, and a lower bound using probabilistic methods, advancing understanding of multi-color graph Ramsey theory.
Contribution
It offers new bounds and exact values for set-coloring Ramsey numbers of specific graphs, and introduces a lower bound via Lovász Local Lemma for general graphs.
Findings
Exact values for stars, paths, matchings, etc.
Bounds for set-coloring Ramsey numbers of various graphs.
A lower bound established using Lovász Local Lemma.
Abstract
The \textit{set-coloring Ramsey number} is the least such that every coloring contains a monochromatic copy of , that is, a color such that for every . If , then we write for short. In 2022, Le asked to find lower and upper bounds for with various kinds of graphs such as stars, paths, cycles, etc. In this paper, we obtain exact values or bounds for the set-coloring Ramsey numbers of stars, paths, matchings, etc. By Lov\'{a}sz Local Lemma, we give a lower bound for the set-coloring Ramsey number for general graphs.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Graph Labeling and Dimension Problems
