2021/11/03 by Akbar Davoodi, Davoodi, Akbar, Ramin Javadi +5
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2111.02065
openalex publication_date 2021/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given graphs F1, F2 and G, we say that G is Ramsey for (F1,F2) and we write G→(F1, F2), if for every edge coloring of G by red and blue, there is either a red copy of F1 or a blue copy of F2 in G. The size Ramsey number r(F1, F2) is defined as the minimum number of edges of a graph G such that G→(F1, F2). This paper provides the exact value of r(F1, F2) for many pairs (F1, F2) of star forests, giving a partial solution to a conjecture of Burr et al. (Ramsey-minimal graphs for multiple copies, Indagationes Mathematicae, 81(2) (1978), 187-195).