On a Conjecture of Graph Parameters Ramsey Theory - Si, Yuan (International Journal of Mathematics And its Applications, 2023)
For graph parameters f_1,f_2,…, f_k and positive integers n_1,n_2,…,n_k, the graph parameters Ramsey number (f_1,f_2,…, f_k)(n_1,n_2,…, n_k) is the minimum positive integer n such that for any factorization of complete graph K_n=_i=1^kG_i, K_n contains at least one subgraph G_i satisfying f_i(G_i)n_i, 1ik. In this paper, we focus on a conjecture of graph parameters Ramsey number (a_1,χ_1)(m,n), where a_1(G) is edge arboricity of graph G and χ_1(G) is edge chromatic number of graph G. We prove that this conjecture is true in some special cases and discuss a possible way to solve this conjecture.