Two classical theorems of Ghouila-Houri and Berge characterize total unimodularity and balancedness in terms of equitable bicolorings and bicolorings, respectively. In this paper, we prove a bicoloring result that provides a common generalization of these two theorems. A 0; 1 matrix is balanced if it does not contain a square submatrix with exactly two nonzero entries per row and per column suc...

For posets P and Q, extremal saturation problems about weak strong P-free subposets of Q have been studied mostly in the case is Boolean poset Qn, all subsets an n-element set ordered by inclusion. In this paper, we study some instances problem with being grid, its connections to forbidden submatrix problem.

We consider the following general hidden hubs model: an n × n random matrix A with a subset S of k special rows (hubs): entries in rows outside S are generated from the (Gaussian) probability distribution p0 ∼ N(0, σ 0); for each row in S, some k of its entries are generated from p1 ∼ N(0, σ 1), σ1 > σ0, and the rest of the entries from p0. The special rows with higher variance entries can be v...

The recursive inverse eigenvalue problem for matrices is studied where for each leading principle submatrix an eigenvalue and associated left and right eigenvectors are assigned Existence and uniqueness results as well as explicit formulas are proven and applications to nonnegative matrices Z matrices M matrices symmetric matrices Stieltjes matrices and inverse M matrices are considered

We consider a hierarchy of four classes of interval digraphs, or equivalently four classes of 0,1-matrics. We provide forbidden submatrix characterizations separating the successive classes. The largest class is the set of (adjacency matrices of) interval digraphs; the smallest is the set of (adjacency matrices of) unit interval digraphs.

Recently Xu 13] proposed a new algorithm for computing a Jacobi matrix of order 2n with a given n n leading principal submatrix and with 2n prescribed eigenvalues that satisfy certain conditions. We compare this algorithm to a scheme proposed by Boley and Golub 2], and discuss a generalization that allows the conditions on the prescribed eigenvalues to be relaxed.