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On optimal orientations of complete tripartite graphs
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Type
Article
Citation
Wong, H., & Tay, E. G. (2021). On optimal orientations of complete tripartite graphs. Australasian Journal of Combinatorics, 80(1), 30–47.
https://ajc.maths.uq.edu.au/pdf/80/ajc_v80_p030.pdf
https://ajc.maths.uq.edu.au/pdf/80/ajc_v80_p030.pdf
Abstract
Given a connected and bridgeless graph G, let D(G) be the family of strong orientations of G. The orientation number of G is defined to be đ(G) := min{d(D) | D ∈ D(G)}, where ,d(D) is the diameter of the digraph D. In this paper, we focus on the orientation number of complete tripartite graphs. We prove a conjecture raised by Rajasekaran and Sampathkumar. Specifically, for q ≥ p ≥ 3, if đ(K(2, p, q)) = 2, then q ≤ (p└p/2┘). We also present some sufficient conditions on p and q for đ(K(p, p, q)) = 2.
Date Issued
2021
Publisher
Combinatorial Mathematics Society of Australasia
Journal
Australasian Journal of Combinatorics