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 University

Document Type

Article

Publication Date

2014

Publication Title

Theory and Applications of Graphs

DOI

10.20429/tag.2014.010102

ISSN

2470-9859

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 $k^{2}$.

Comments

Creative Commons License

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

Recommended Citation

Holliday, Rebecca, Colton Magnant, Pouria Salehi Nowbandegani. 2014. "Note on Rainbow Connection in Oriented Graphs with Diameter 2." Theory and Applications of Graphs, 1 (1): 1-6: Georgia Southern University Press. doi: 10.20429/tag.2014.010102
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/752