Maximum Oriented Forcing Number for Complete Graphs

Authors

Yair Caro, University of Haifa-OranimFollow
Ryan Pepper, University of Houston - DowntownFollow

Abstract

The maximum oriented k-forcing number of a simple graph G, written MOF_k(G), is the maximum directed k-forcing number among all orientations of G. This invariant was recently introduced by Caro, Davila and Pepper in [6], and in the current paper we study the special case where G is the complete graph with order n, denoted K_n . While MOF_k(G) is an invariant for the underlying simple graph G, MOF_k(K_n) can also be interpreted as an interesting property for tournaments. Our main results further focus on the case when ,em>k=1. These include a lower bound on MOF(K_n) of roughly ¾n, and for n ≥ 2 , a lower bound of n - \frac{2n}{\log_2(n)}. We also consider various lower bounds on the maximum oriented k-forcing number for the closely related complete q-partite graphs.

Creative Commons License

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

Recommended Citation

Caro, Yair and Pepper, Ryan (2019) "Maximum Oriented Forcing Number for Complete Graphs," Theory and Applications of Graphs: Vol. 6: Iss. 1, Article 6.
DOI: 10.20429/tag.2019.060106
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol6/iss1/6