Journal of Combinatorial Optimization

, Volume 27, Issue 3, pp 530–540 | Cite as

The Pfaffian property of Cartesian products of graphs

  • Fuliang Lu
  • Lianzhu Zhang


Suppose that G=(V,E) is a graph with even vertices. An even cycle C is a nice cycle of G if GV(C) has a perfect matching. An orientation of G is a Pfaffian orientation if each nice cycle C has an odd number of edges directed in either direction of the cycle. Let P n and C n denote the path and the cycle on n vertices, respectively. In this paper, we characterize the Pfaffian property of Cartesian products G×P 2n and G×C 2n for any graph G in terms of forbidden subgraphs of G. This extends the results in (Yan and Zhang in Discrete Appl Math 154:145–157, 2006).


Perfect matchings Pfaffian graphs Cartesian products of graphs 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.School of SciencesLinyi UniversityLinyiChina
  2. 2.School of Mathematical SciencesXiamen UniversityXiamenChina

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