In this note, we provide a sharp upper bound on the rainbow connection number of tournaments of diameter 2. For a tournament Τ of diameter 2, we show 2 ≤ → rc (Τ) ≤ 3. Furthermore, we provide a general upper bound on the rainbow κ-connection number of tournaments as a simple example of the probabilistic method. Finally, we show that an edge-colored tournament of κthdiameter 2 has rainbow κ-connection number at most approximately κ2.
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Holliday, Rebecca; Magnant, Colton; and Salehi Nowbandegani, Pouria
"Note on Rainbow Connection in Oriented Graphs with Diameter 2,"
Theory and Applications of Graphs: Vol. 1:
1, Article 2.
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol1/iss1/2