5 problems

Let $n\ge3$ and $k\ge2$. For each $i\in\{0,1,\ldots,n-2\}$, let $G_i=P_{2i+3}$, and let $G_{n-1}$ be either $C_{2n}$ or $P_{2n+1}$. Choose integers $i_1,\ldots,i_k$ satisfying … He…

Gallai-Ramsey conjecture for books. For $k\geq 2$,

Let $H$ be a connected bipartite graph, let $R(H,H)=R$ be its two-color Ramsey number, and let $s(H)$ denote the parameter used in the source. The general bipartite Gallai-Ramsey c…

Let $P_3$ be the path on three vertices, and let $gr_k(K_3:n_1P_3,\ldots,n_kP_3)$ denote the corresponding Gallai-Ramsey number. For positive integers $k,n_1,n_2,\ldots,n_k$ with…

Let $P_3$ denote the path on three vertices, and let $gr_k(K_3:n_1P_3, \ldots,n_kP_3)$ be the corresponding multicolor Gallai-Ramsey number. For positive integers…