Geodesic
Maximal nests of subspaces, the matrix Bruhat decomposition, and the marriage theorem---with an application to graph coloring
The electronic journal of linear algebra, Tome 9 (2002), pp. 118-121.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Using the celebrated marriage theorem of P. Hall, we give an elementary combinatorial proof of the theorem that asserts that given two maximal nests ${\cal N}_1$ and ${\cal N}_2$ in a finite-dimensional vector spce $V$, there is an ordered basis of $V$ that generates ${\cal N}_1$ and a permutation of that ordered basis that generates ${\cal N}_2$. From this theorem one easily obtains the matrix Bruhat decomposition. A generalization to matroids is discussed, and an application to graph coloring is given.
Classification : 15A03, 05C15, 05B35
Keywords: nests of subspaces, matrix Bruhat decomposition, marriage theorem, graph colorings, matroids 
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Brualdi, Richard A. Maximal nests of subspaces, the matrix Bruhat decomposition, and the marriage theorem---with an application to graph coloring. The electronic journal of linear algebra, Tome 9 (2002), pp. 118-121. http://geodesic.mathdoc.fr/item/ELA_2002__9__a13/