Maximal nests of subspaces, the matrix Bruhat decomposition, and the marriage theorem---with an application to graph coloring.
Discrepancy of matrices of zeros ond ones.
A Bruhat order for the class of -matrices with row sum vector and column sum vector .
Two extremal problems in graph theory.
Landau's and Rado's theorems and partial tournaments.
Perfect matching preservers.
Hall exponents of Boolean matrices
On minimal regular digraphs with girth 4
Hall exponents of matrices, tournaments and their line digraphs
Let be a square -matrix. Then is a Hall matrix provided it has a nonzero permanent. The Hall exponent of is the smallest positive integer , if such exists, such that is a Hall matrix. The Hall exponent has received considerable attention, and we both review and expand on some of its properties. Viewing as the adjacency matrix of a digraph, we prove several properties of the Hall exponents of line digraphs with some emphasis on line digraphs of tournament (matrices).
On the Spectral Radius of Connected Graphs
Doubly stochastic matrices and the Bruhat order
The Bruhat order is defined in terms of an interchange operation on the set of permutation matrices of order which corresponds to the transposition of a pair of elements in a permutation. We introduce an extension of this partial order, which we call the stochastic Bruhat order, for the larger class of doubly stochastic matrices (convex hull of permutation matrices). An alternative description of this partial order is given. We define a class of special faces of induced by permutation matrices,...
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