✦ LIBER ✦

A note on the total unimodularity of matrices

✍ Scribed by Manfred W. Padberg

Publisher: Elsevier Science
Year: 1976
Tongue: English
Weight: 778 KB
Volume: 14
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(76)90041-8

No coin nor oath required. For personal study only.

✦ Synopsis

A ri43xsaty and sufficient chiiriweritation lrrf totally unimodular matrices is given ick is derived from a nixewrq~ condbtion for totdi unimodularity due to Camion. II~ ~~~~~~~~~~~~tj~n is then used in cunnectirsrh with a theorem of Hoffman and Kruskal to provide an elcment~ry prwf of the characteaization of totally unimoduhr matrices in terms of forbidden submatrices due to Camion.

📜 SIMILAR VOLUMES

On totally unimodular matrices

✍ A. Tamir 📂 Article 📅 1976 🏛 John Wiley and Sons 🌐 English ⚖ 431 KB

## Abstract Conditions for a matrix to be totally unimodular, due to Camion, are applied to extend and simplify proofs of other characterizations of total unimodularity.

A hierarchy of totally unimodular matric

A hierarchy of totally unimodular matrices

✍ Martin Loebl; Svatopluk Poljak 📂 Article 📅 1989 🏛 Elsevier Science 🌐 English ⚖ 556 KB

We say that a totally unimodular matrix is k-totally unimodular (k-TU), if every matrix obtained from it by setting to zero a subset of at most k entries is still totally unimodular. We present the following results. (i) A matrix is restricted unimodular if and only if it is 3-TU, (ii) for a 2-TU m

A Generalization of Tutte's Characteriza

A Generalization of Tutte's Characterization of Totally Unimodular Matrices

✍ J.F. Geelen 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 386 KB

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 unimodula

A Note on Unimodular Rows

✍ N.Mohan Kumar 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 153 KB

A Note on Optimal Unimodular Lattices

✍ J.H Conway; N.J.A Sloane 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 169 KB

The highest possible minimal norm of a unimodular lattice is determined in dimensions n 33. There are precisely five odd 32-dimensional lattices with the highest possible minimal norm (compared with more than 8.10 20 in dimension 33). Unimodular lattices with no roots exist if and only if n 23, n{25

A note on unimodular congruence of graph

A note on unimodular congruence of graphs

✍ Russell Merris 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 407 KB