Theory and Applications of Graphs

Article Title

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