On the set-coloring Ramsey numbers of graphs
Abstrak
The \textit{set-coloring Ramsey number} $\mathrm{R}_{r, s}(G_1,G_2,...,G_r)$ is the least $n \in \mathbb{N}$ such that every coloring $χ: E\left(K_n\right) \rightarrow\binom{[r]}{s}$ contains a monochromatic copy of $G_i$, that is, a color $i \in[r]$ such that $i \in χ(e)$ for every $e \in E(G_i)$. If $G_1=G_2=\cdots=G_r=G$, then we write $\mathrm{R}_{r,s}(G)$ for short. In 2022, Le asked to find lower and upper bounds for $\mathrm{R}_{s, t}(G)$ with various kinds of graphs $G$ 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 Lovász Local Lemma, we give a lower bound for the set-coloring Ramsey number for general graphs.
Topik & Kata Kunci
Penulis (2)
Mengya He
Yaping Mao
Akses Cepat
- Tahun Terbit
- 2025
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓