# Distance Between α-Orientations of Plane Graphs by Facial Cycle Reversals

• Wei Juan Zhang
• Jian Guo Qian
• Fu Ji Zhang
Article

## Abstract

Cycle reversal had been shown as a powerful method to deal with the relation among orientations of a graph since it preserves the out-degree of each vertex and the connectivity of the orientations. A facial cycle reversal on an orientation of a plane graph is an operation that reverses all the directions of the edges of a directed facial cycle. An orientation of a graph is called an α- orientation if each vertex admits a prescribed out-degree. In this paper, we give an explicit formula for the minimum number of the facial cycle reversals needed to transform one α-orientation into another for plane graphs.

## Keywords

α-Orientation facial cycle reversal distance plane graph

## MR(2010) Subject Classification

05C10 05C76 05C12

## Notes

### Acknowledgements

The authors would like to thank the anonymous reviewers for their constructive comments and suggestions.

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© Institute of Mathematics, Academy of Mathematics and Systems Science (CAS), Chinese Mathematical Society (CAS) and Springer-Verlag GmbH Germany, part of Springer Nature 2018

## Authors and Affiliations

• Wei Juan Zhang
• 1
• 2
• Jian Guo Qian
• 1
Email author
• Fu Ji Zhang
• 1
1. 1.School of Mathematical SciencesXiamen UniversityXiamenP. R. China
2. 2.School of Mathematical SciencesXinjiang Normal UniversityUrumqiP. R. China