Given two graphs G and H, the k-colored Gallai–Ramsey number \(gr_k(G : H)\) is defined to be the minimum integer n such that every k-coloring of the complete graph on n vertices contains either a rainbow copy of G or a monochromatic copy of H. In this paper, we consider \(gr_k(K_3 : H)\), where H is a connected graph with five vertices and at most six edges. There are in total thirteen graphs in this graph class, and the Gallai–Ramsey numbers for eight of them have been studied step by step in several papers. We determine all the Gallai–Ramsey numbers for the remaining five graphs, and we also obtain some related results for a class of unicyclic graphs. As applications, we find the mixed Ramsey spectra \(S(n; H, K_3)\) for these graphs by using the Gallai–Ramsey numbers.

给定两个图G和H，将k色的Gallai–Ramsey数\（gr_k（G：H）\）定义为最小整数n，这样，在n个顶点上完整图的每个k色都包含一个彩虹的复制ģ或的单色副本ħ。在本文中，我们考虑\（gr_k（K_3：H）\），其中H是具有五个顶点和最多六个边的连接图。该图类中总共有13张图，其中几篇论文逐步研究了其中8张的Gallai–Ramsey数。我们确定其余五张图的所有Gallai–Ramsey数，并且我们还获得了一类单环图的相关结果。作为应用，我们通过使用Gallai–Ramsey数找到这些图的混合Ramsey光谱\（S（n; H，K_3）\）。