English

Oriented diameter of the complete tripartite graph (III)

Combinatorics 2025-02-24 v1

Abstract

Given a bridgeless graph GG, let D(G)\mathbb{D}(G) be the set of all strong orientations of GG, and define the oriented diameter f(G)f(G) of GG to be the minimum of diameters diam(D)diam(D) among all the strong orientations DD(G)D\in \mathbb{D}(G), i.e., f(G)=min{diam(D)DD(G)}f(G)=\min\{diam(D)\mid D\in \mathbb{D}(G)\}. In this paper, we determine the oriented diameter of complete tripartite graph K(3,p,q)K(3,p,q) for p5p\geqslant 5. Combining with the previous results, the oriented diameter of complete tripartite graph K(3,p,q)K(3,p,q) are known.

Cite

@article{arxiv.2502.14903,
  title  = {Oriented diameter of the complete tripartite graph (III)},
  author = {Jing Liu and Guang Rao and Hui Zhou},
  journal= {arXiv preprint arXiv:2502.14903},
  year   = {2025}
}
R2 v1 2026-06-28T21:51:54.058Z