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

A graph 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 ....

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Bibliographic Details
Published inJournal of combinatorial optimization Vol. 35; no. 3; pp. 740 - 753
Main Authors Feng, Xing, Zhang, Lianzhu, Zhang, Mingzu
Format Journal Article
LanguageEnglish
Published New York Springer US 01.04.2018
Springer Nature B.V
Subjects
Combinatorics
Convex and Discrete Geometry
Graph matching
Graph theory
Graphs
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Orientation
Theory of Computation
Bipartite graph
Perfect matching
Algorithm
Pfaffian orientation
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ISSN1382-6905
1573-2886
DOI10.1007/s10878-017-0207-0

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Summary:A graph 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 ) 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.
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-017-0207-0