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I'm learning network and transportation model. The question is not from my homework. I'm just curious about:

In a graph $G$, its incidence matrix $A$ is totally unimodular if and only if $G$ is a bipartite graph.

Could anyone good at proving give a simple provement?

OR

Could anyone provide some related materials?

Rodrigo de Azevedo
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Jill Clover
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1 Answers1

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I suppose you refer to undirected graphs, as the (node-arc-) incidence matrix of a directed graph is always totally unimodular.

Anyways, you'll find a nice proof for your question right at the first hit on Google after querying for "incidence matrix bipartite".

Gabor Retvari
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