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 such that every bridgeless graph with diameter has an orientation with diameter at most . For , they proved that . Until recently, Kwok, Liu and West improved the above bounds by proving 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