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Grossman conjectured that $R(G, G) = 2 \cdot |V(G)| - 1$, for all simple connected unicyclic graphs $G$ of odd girth and $|V(G)| \geq 4$. 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