Journal or Book Title
Linear Algebra and its Applications
A list of positions in an n×n real matrix (a pattern) is said to have P-completion if every partial P-matrix that specifies exactly these positions can be completed to a P-matrix. We extend the work of C.R. Johnson, B.K. Kroschel [Electron. J. Linear Algebra Appl. 241–243 (1996) 655–657] by proving that a larger class of patterns has P-completion, including any 4×4 pattern with eight or fewer off-diagonal positions. We also show that any pattern whose digraph contains a minimally chordal symmetric-Hamiltonian induced subdigraph does not have P-completion.
This manuscript version is made available under the CCBY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
DeAlba, Luz M. and Hogben, Leslie, "Completions of P-matrix patterns" (2000). Mathematics Publications. 72.