Improved Upper Bounds for Gallai-Ramsey Numbers of Paths and CyclesJournal of Graph Theory
AbstractGiven a graph G and a positive integer k, define the Gallai–Ramsey 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 Gallai–Ramsey numbers for paths and cycles. All these upper bounds now have the best possible order of magnitude as functions of k.
Citation InformationMartin Hall, Colton Magnant, Kenta Ozeki and Masao Tsugaki. "Improved Upper Bounds for Gallai-Ramsey Numbers of Paths and Cycles" Journal of Graph Theory Vol. 75 Iss. 1 (2014) p. 59 - 74
Available at: http://works.bepress.com/colton_magnant/39/