Note on Rainbow Connection in Oriented Graphs with Diameter 2

Authors

Rebecca Holliday, Georgia Southern UniversityFollow
Colton Magnant, Georgia Southern UniversityFollow
Pouria Salehi Nowbandegani, Georgia Southern UniversityFollow

Publication Date

2014

Abstract

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 κ^thdiameter 2 has rainbow κ-connection number at most approximately κ².

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Holliday, Rebecca; Magnant, Colton; and Salehi Nowbandegani, Pouria (2014) "Note on Rainbow Connection in Oriented Graphs with Diameter 2," Theory and Applications of Graphs: Vol. 1: Iss. 1, Article 2.
DOI: 10.20429/tag.2014.010102
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol1/iss1/2