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