Geodesic
Graph characterization of fully indecomposable nonconvertible (0, 1)-matrices with minimal number of ones
Ars Mathematica Contemporanea, Tome 17 (2019) no. 1, pp. 141-151.

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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.
DOI : 10.26493/1855-3974.1517.e42
Keywords: Permanent, indecomposable matrices, graphs 
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Mikhail Budrevich; Gregor Dolinar; Alexander Guterman; Bojan Kuzma. Graph characterization of fully indecomposable nonconvertible (0, 1)-matrices with minimal number of ones. Ars Mathematica Contemporanea, Tome 17 (2019) no. 1, pp. 141-151. doi : 10.26493/1855-3974.1517.e42. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1517.e42/

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