Matrices with prescribed row, column and block sums
type: Item
instance of: scholarly article
title: Matrices with prescribed row, column and block sums
zbMATH Open document ID: 0667.05012
DOI: 10.1007/BF02122798
author: A. A. Chernyak
author: Zhanna A. Chernyak
published in: Combinatorica
publication date: 1988-01-01T00:00:00Z
review text: The properties of graphical integer-pair sequences (edge degree sequences) generalizing the concept of the well-known degree sequences are considered. In this paper it is proved that from any two integral symmetric matrices with given block partition and prescribed row, column and block sums one can pass by interchanges preserving these sums, to the other two ones falling ``close'' together as much as possible. The well- known Changphaisan's interchange theorem and Kleitman-Wang-Kundu's k- factor theorem are obtained as corollaries. It is shown that any realization of r-graphical integer-pair sequence can be obtained from any other one by r-switchings, preserving edge degrees. This result allows also to determine s-complete properties.
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 05C99
zbMATH DE Number: 4091520
zbMATH Keywords: graphical integer-pair sequences
zbMATH Keywords: edge degree sequences
zbMATH Keywords: r-switchings
reviewed by: S. S. Agayan
MaRDI profile type: Publication
cites work: Q3927278
cites work: Matrices of zeros and ones with fixed row and column sum vectors
cites work: Conditions for sequences to be r-graphic
cites work: Q3039401
cites work: Q3964615
cites work: Q3931446
cites work: Unidigraphic and unigraphic degree sequences through uniquely realizable integer-pair sequences
cites work: Q3859816
cites work: Some Properties of Graphs with Multiple Edges
cites work: Algorithms for constructing graphs and digraphs with given valences and factors
cites work: The k-factor conjecture is true
cites work: Relations between graphs and integer-pair sequences
cites work: Combinatorial Properties of Matrices of Zeros and Ones
cites work: The network flows approach for matrices with given row and column sums
full work available at URL: https://doi.org/10.1007/bf02122798
OpenAlex ID: W2009692878
description: scientific article; zbMATH DE number 4091520