A note on multiflow locking theorem

A note on multiflow locking theorem

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Article ID: iaor20105099
Volume: 53
Issue: 2
Start Page Number: 149
End Page Number: 156
Publication Date: Jun 2010
Journal: Journal of the Operations Research Society of Japan
Authors:
Abstract:

This note addresses the undirected multiflow (multicommodity flow) theory. A multiflow in a network with terminal set T can be regarded as a single commodity (A, T \A)-flow for any nonempty proper subset AT by ignoring flows not connecting A and T \ A. A set system A on T is said to be lockable if for every network having T as terminal set there exists a multiflow being simultaneously a maximum (A, T \A)-flow for every AA. The multiflow locking theorem, due to Karzanov and Lomonosov, says that A is lockable if and only if it is 3-cross-free.

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