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An $$O(|E(G)|^2)$$ O ( | E ( G ) | 2 ) algorithm for recognizing Pfaffian graphs of a type of bipartite graphs

Author

Listed:
  • Xing Feng

    (Xiamen University)

  • Lianzhu Zhang

    (Xiamen University)

  • Mingzu Zhang

    (Xiamen University)

Abstract

A graph $$G=(V,E)$$ G = ( V , E ) with even number vertices is called Pfaffian if it has a Pfaffian orientation, namely it admits an orientation such that the number of edges of any M-alternating cycle which have the same direction as the traversal direction is odd for some perfect matching M of the graph G. In this paper, we obtain a necessary and sufficient condition of Pfaffian graphs in a type of bipartite graphs. Then, we design an $$O(|E(G)|^2)$$ O ( | E ( G ) | 2 ) algorithm for recognizing Pfaffian graphs in this class and constructs a Pfaffian orientation if the graph is Pfaffian. The results improve and generalize some known results.

Suggested Citation

  • Xing Feng & Lianzhu Zhang & Mingzu Zhang, 2018. "An $$O(|E(G)|^2)$$ O ( | E ( G ) | 2 ) algorithm for recognizing Pfaffian graphs of a type of bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 35(3), pages 740-753, April.
    • Handle: RePEc:spr:jcomop:v:35:y:2018:i:3:d:10.1007_s10878-017-0207-0
    DOI: 10.1007/s10878-017-0207-0
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    References listed on IDEAS

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    1. Fuliang Lu & Lianzhu Zhang, 2014. "The Pfaffian property of Cartesian products of graphs," Journal of Combinatorial Optimization, Springer, vol. 27(3), pages 530-540, April.
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