Consider the graph consisting of a triangle with a pendant edge. We describe the structure of rainbow -free edge colorings of a complete graph and provide some corresponding Gallai–Ramsey results. In particular, we extend a result of Gallai to find a partition of the vertices of a rainbow -free colored complete graph with a limited number of colors between the parts. We also extend some Gallai–Ramsey results of Chung and Graham, Faudree et al. and Gyárfás et al.
Available at: http://works.bepress.com/colton_magnant/17/