The Ramsey numbers for disjoint unions of trees (Q856882)

In the paper the Ramsey numbers \(R(G,H)\) are investigated in the case when \(G\) and \(H\) are stars \(S_n\), wheels \(W_n\), trees \(T_n\), or complete graphs \(K_n\). For example it is shown that if \(n\geq 3\), then \(R(k S_n,W_4)\) is equal to \((k+1)n\) if \(n\) is even and \(k\geq 2\), and it is equal to \((k+1)n-1\) if \(n\) is odd and \(k\geq 1\). Further it is shown that under some conditions, \[ R(\bigcup_{i=1}^k T_{n_i}, K_m)= R(T_{n_k},K_m)+\sum_{i=1}^{k-1}n_i. \]