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Note on rainbow connection in oriented graphs with diameter 2
Theory and Applications of Graphs
  • Rebecca Holliday, Georgia Southern University
  • Colton Magnant, Georgia Southern University
  • Pouria Salehi Nowbandegani, Georgia Southern University
Abstract

In this note, we provide a sharp upper bound on the rainbow connection number of tournaments of diameter $2$. For a tournament $T$ of diameter $2$, we show $2 \leq \overrightarrow{rc}(T) \leq 3$. Furthermore, we provide a general upper bound on the rainbow $k$-connection number of tournaments as a simple example of the probabilistic method. Finally, we show that an edge-colored tournament of $k^{th}$ diameter $2$ has rainbow $k$-connection number at most approximately $k^{2}$.

Citation Information
Rebecca Holliday, Colton Magnant and Pouria Salehi Nowbandegani. "Note on rainbow connection in oriented graphs with diameter 2"
Available at: http://works.bepress.com/colton_magnant/35/