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Abstract: Given two graphs F_1 and F_2, their size Ramsey number, denoted by r̂(F_1, F_2), is the minimum number of edges of a graph G such that for any edge coloring of G by colors red and blue, G contains either a red copy of F1 or a blue copy of F2. In this paper, we deal with the size Ramsey number of star forests (disjoint union of stars) and following a conjecture by Burr, Erdős, Faudree, Rousseau, and Schelp in 1978, we determine the exact value of r̂(⊔_{i = 1}^s K_{1, ni}, ⊔_{i = 1}^t K_{1, mi}) in several cases including when either m_i’s and n_i’s are odd, or s = 1 or s = 2 and n_1 = n_2.
Keywords: size Ramsey number, star forest, Ramsey minimal graph
Published in RUP: 21.10.2025; Views: 390; Downloads: 4
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