On the minors of an incidence matrix and Smith normal form
type: Item
instance of: scholarly article
title: On the minors of an incidence matrix and Smith normal form
zbMATH Open document ID: 0819.05043
DOI: 10.1016/0024-3795(93)00173-W
author: Jerrold W. Grossman
author: Devadatta M. Kulkarni
author: Irwin E. Schochetman
published in: Linear Algebra and its Applications
publication date: 1995-05-11T00:00:00Z
review text: The possible minors of a vertex-edge incidence matrix of an undirected loopless graph are completely determined. Then the maximum and minimum absolute values of the maximal minors of the incidence matrix as well as its Smith normal form are determined. The results are used to obtain a sufficient condition for a system of equations (whose coefficient matrix is an incidence matrix) to admit an integer solution.
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 68R10
Mathematics Subject Classification ID: 90C10
zbMATH DE Number: 753870
zbMATH Keywords: integer programming
zbMATH Keywords: minors
zbMATH Keywords: incidence matrix
zbMATH Keywords: Smith normal form
MaRDI profile type: Publication
cites work: Bicycles and Spanning Trees
cites work: Quasi-symmetric designs and the Smith normal form
cites work: Combinatorial matrix theory
cites work: The application of invariant theory to the existence of quasi-symmetric designs
cites work: Geometric invariants for quasi-symmetric designs
cites work: The point-arboricity of a graph
cites work: On the maximal number of independent circuits in a graph
cites work: Maximum matching and a polyhedron with 0,1-vertices
cites work: Paths, Trees, and Flowers
cites work: Q5342984
cites work: Q4198056
cites work: Dioïds and semirings: Links to fuzzy sets and other applications
cites work: Unimodular equivalence of graphs
cites work: Maximizing Submodular Set Functions: Formulations and Analysis of Algorithms
cites work: Q5686064
cites work: Q5512801
cites work: Q3818127
description: scientific article; zbMATH DE number 753870