A shortest augmenting path method for solving minimal perfect matching problems

Networks ◽  
1981 ◽  
Vol 11 (4) ◽  
pp. 379-390 ◽  
Author(s):  
Ulrich Derigs
Keyword(s):  
Perfect Matching ◽  
Matching Problems ◽  
Augmenting Path

Augmenting trail theorem for the maximum 1-2 matching problem

2017 ◽  
Vol 09 (04) ◽  
pp. 1750056 ◽  
Author(s):  
Hiroki Izumi ◽  
Sennosuke Watanabe ◽  
Yoshihide Watanabe
Keyword(s):  
Bipartite Graph ◽  
Bipartite Graphs ◽  
Matching Problem ◽  
Matching Problems ◽  
Augmenting Path

We consider the maximum 1-2 matching problem in bipartite graphs. The notion of the augmenting trail for the 1-2 matching problem, which is the extension of the notion of the augmenting path for the 1-1 matching problem is introduced. The main purpose of the present paper is to prove “the augmenting trail theorem” for the 1-2 matching problem in the bipartite graph, which is an analogue of the augmenting path theorem by Bergé for the usual 1-1 matching problems.

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