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For two graphs $G,H$, the \emph{Ramsey number} $r(G,H)$ is the minimuminteger $n$ such that any red/blue edge-coloring of $K_n$ contains either a redcopy of $G$ or a blue copy of $H$. For two graphs $G,H$, the\emph{Gallai-Ramsey number} $\operatorname{gr}_k(G:H)$ is defined as theminimum integer $n$ such that any $k$-edge-coloring of $K_n$ must containeither a rainbow copy of $G$ or a monochromatic copy of $H$. In this paper, theclassical Ramsey numbers of linear forest versus kipas are obtained. We obtainthe exact values of $\operatorname{gr}_k(G:H)$, where $H$ is either a path or akipas and $G\in\{K_{1,3},P_4^+,P_5\}$ and $P_4^+$ is the graph consisting of$P_4$ with one extra edge incident with inner vertex.

Ramsey and Gallai-Ramsey numbers for linear forests and kipas