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

  • Wei Juan Zhang
  • Jian Guo QianEmail author
  • Fu Ji Zhang
Article
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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 

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Notes

Acknowledgements

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

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Copyright information

© 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

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