Contract grant sponsor: Georgia Southern Faculty Research Committee—Research Competition Award (to C. M.); Contract grant sponsor: Chinese Academy of Sciences Fellowship for Young International Scientists (to M. T.); Contract grant number: 2012Y1JA0004.
Improved Upper Bounds for Gallai–Ramsey Numbers of Paths and Cycles
Version of Record online: 31 JAN 2013
© 2013 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 75, Issue 1, pages 59–74, January 2014
How to Cite
Hall, M., Magnant, C., Ozeki, K. and Tsugaki, M. (2014), Improved Upper Bounds for Gallai–Ramsey Numbers of Paths and Cycles. J. Graph Theory, 75: 59–74. doi: 10.1002/jgt.21723
- Issue online: 22 OCT 2013
- Version of Record online: 31 JAN 2013
- Manuscript Revised: 6 DEC 2012
- Manuscript Received: 1 FEB 2012
- Georgia Southern Faculty Research Committee—Research Competition
- Chinese Academy of Sciences Fellowship for Young International Scientists. Grant Number: 2012Y1JA0004
- rainbow triangle;
- Gallai coloring;
- Gallai Ramsey
Given 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.