New Diagonal Graph Ramsey Numbers of Unicyclic Graphs

Authors

Richard M. Low, San Jose State UniversityFollow
Ardak Kapbasov, San Jose State UniversityFollow

Abstract

Grossman conjectured that R(G, G) = 2 ⋅ |V(G)| - 1, for all simple connected unicyclic graphs G of odd girth and |V(G)| ≥ 4. In this note, we prove his conjecture for various classes of G containing a triangle. In addition, new diagonal graph Ramsey numbers are calculated for some classes of simple connected unicyclic graphs of even girth.

Creative Commons License

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

Recommended Citation

Low, Richard M. and Kapbasov, Ardak (2023) "New Diagonal Graph Ramsey Numbers of Unicyclic Graphs," Theory and Applications of Graphs: Vol. 10: Iss. 1, Article 9.
DOI: 10.20429/tag.2023.10109
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol10/iss1/9