Gallai-Ramsey Numbers for Monochromatic Triangles or 4-Cycles

Gallai-Ramsey numbers often consider edge-colorings of complete graphs in which there are no rainbow triangles. Within such colored complete graphs, the goal is to look for specified monochromatic subgraphs. We consider an “off diagonal” case of this concept by looking for either a monochromatic K3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{3}$$\end{document} in one of some set of colors or a monochromatic C4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{4}$$\end{document} in one of some other set of colors.