Graph characterization of fully indecomposable nonconvertible (0, 1)-matrices with minimal number of ones

Mikhail Budrevich, Gregor Dolinar, Alexander Guterman, Bojan Kuzma

Abstract


Let A be a (0, 1)-matrix such that PA is indecomposable for every permutation matrix P and there are 2n + 3 positive entries in A. Assume that A is also nonconvertible in a sense that no change of signs of matrix entries, satisfies the condition that the permanent of A equals to the determinant of the changed matrix.

We characterized all matrices with the above properties in terms of bipartite graphs. Here 2n + 3 is known to be the smallest integer for which nonconvertible fully indecomposable matrices do exist. So, our result provides the complete characterization of extremal matrices in this class.


Keywords


Permanent, indecomposable matrices, graphs

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DOI: https://doi.org/10.26493/1855-3974.1517.e42

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications