Matrices with prescribed row, column and block sums
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.
scientific article; zbMATH DE number 4091520
scientific article