A linear upper bound on the zero-sum Ramsey number of forests in ℤ_p

2025/12/06 by Colucci, Lucas, D'Emidio, Marco · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory

paper · doi:10.48550/arxiv.2512.06229

openalex publication_date 2025/12/06 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28

Abstract

Let m be a positive integer and let G be a graph. The zero-sum Ramsey number R(G,ℤ_m) is the least integer N (if it exists) such that for every edge-coloring χ : E(K_N) → ℤ_m one can find a copy of G in K_N such that ∑_{e ∈ E(G)}χ(e) = 0. In this paper, we show that, for every prime p, R(F,ℤ_p)≤ n+9p-12 for every forest F in n≥ 3p²-12p+11 vertices with p| e(F) without isolated vertices.

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• A linear upper bound for zero-sum Ramsey numbers of bounded degree graphs

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