Flip-distance between \alpha-orientations of graphs embedded on plane and sphere
Combinatorics
2017-06-06 v1
Abstract
Felsner introduced a cycle reversal, namely the `flip' reversal, for \alpha-orientations (i.e., each vertex admits a prescribed out-degree) of a graph G embedded on the plane and further proved that the set of all the \alpha-orientations of G carries a distributive lattice with respect to the flip reversals. In this paper, we give an explicit formula for the minimum number of flips needed to transform one \alpha-orientation into another for graphs embedded on the plane or sphere, respectively.
Cite
@article{arxiv.1706.00970,
title = {Flip-distance between \alpha-orientations of graphs embedded on plane and sphere},
author = {Weijuan Zhang and Jianguo Qian and Fuji Zhang},
journal= {arXiv preprint arXiv:1706.00970},
year = {2017}
}
Comments
15 pages, 4 figures