English

Note on the oriented diameter of graphs with diameter 3

Combinatorics 2011-09-28 v2

Abstract

In 1978, Chv\'atal and Thomassen showed that every bridgeless graph with diameter 2 has an orientation with diameter at most 6. They also gave general bounds on the smallest value f(d)f(d) such that every bridgeless graph GG with diameter dd has an orientation with diameter at most f(d)f(d). For d=3d=3, they proved that 8f(d)248\leq f(d)\leq 24. Until recently, Kwok, Liu and West improved the above bounds by proving 9f(3)119\leq f(3)\leq 11 in [P.K. Kwok, Q. Liu and D.B. West, Oriented diameter of graphs with diameter 3, J. Combin. Theory Ser.B 100(2010), 265-274]. In this paper, we determine the oriented diameter among the bridgeless graphs with diameter 3 that have minimum number of edges.

Keywords

Cite

@article{arxiv.1109.1056,
  title  = {Note on the oriented diameter of graphs with diameter 3},
  author = {Hengzhe Li and Xueliang Li and Yuefang Sun and Jun Yue},
  journal= {arXiv preprint arXiv:1109.1056},
  year   = {2011}
}

Comments

14 pages

R2 v1 2026-06-21T19:00:12.625Z