Improved Upper Bounds for GallaiRamsey Numbers of Paths and Cycles
Given a graph G and a positive integer k, define the GallaiRamsey number to be the minimum number of vertices n such that any k-edge coloring of contains either a rainbow (all different colored) triangle or a monochromatic copy of G. In this work, we improve upon known upper bounds on the GallaiRamsey numbers for paths and cycles. All these upper bounds now have the best possible order of magnitude as functions of k.
path cycle rainbow triangle gallai coloring gallai ramsey