Theory and Applications of Graphs Theory and Applications of Graphs

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 ≤ −→ rc ( T ) ≤ 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 .