Improved Upper Bounds for Gallai-Ramsey Numbers of Paths and Cycles

Authors

Martin Hall, Georgia Southern UniversityFollow
Colton Magnant, Georgia Southern UniversityFollow
Kenta Ozeki, National Institute of Informatics, Tokyo, JapanFollow
Masao Tsugaki, Chinese Academy of Sciences

Document Type

Article

Publication Date

1-2014

Publication Title

Journal of Graph Theory

DOI

10.1002/jgt.21723

ISSN

1097-0118

Abstract

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.

Recommended Citation

Hall, Martin, Colton Magnant, Kenta Ozeki, Masao Tsugaki. 2014. "Improved Upper Bounds for Gallai-Ramsey Numbers of Paths and Cycles." Journal of Graph Theory, 75 (1): 59-74. doi: 10.1002/jgt.21723
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/298