A General Lower Bound on Gallai-Ramsey Numbers for Non-Bipartite Graphs

Authors

Colton Magnant, Georgia Southern UniversityFollow

Publication Date

2018

Abstract

Given a graph H and a positive integer k, the k-color Gallai-Ramsey number gr_k(K3 : H) is defined to be the minimum number of vertices n for which any k-coloring of the complete graph K_n contains either a rainbow triangle or a monochromatic copy of H. The behavior of these numbers is rather well understood when H is bipartite but when H is not bipartite, this behavior is a bit more complicated. In this short note, we improve upon existing lower bounds for non-bipartite graphs H to a value that we conjecture to be sharp up to a constant multiple.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Magnant, Colton (2018) "A General Lower Bound on Gallai-Ramsey Numbers for Non-Bipartite Graphs," Theory and Applications of Graphs: Vol. 5: Iss. 1, Article 4.
DOI: 10.20429/tag.2018.050104
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol5/iss1/4