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A Generalization of Tutte's Characterization of Totally Unimodular Matrices

✍ Scribed by J.F. Geelen

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
386 KB
Volume
70
Category
Article
ISSN
0095-8956

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✦ Synopsis

dedicated to professor w. t. tutte on the occasion of his eightieth birthday

We characterize the symmetric (0, 1)-matrices that can be signed symmetrically so that every principal submatrix has determinant 0, \1. This characterization generalizes Tutte's famous characterization of totally unimodular matrices. The result can be viewed as an excluded minor theorem for an interesting class of deltamatroids.

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## Abstract In this paper we present a relatively simple proof of Tutt's characterization of graphic matroids. The proof uses the notion of β€˜signed graph’ and it is β€˜graphic’ in the sense that it can be presented almost entirely by drawing (signed) graphs. Β© 1995 John Wiley & Sons, Inc.

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