On the rank of Z_2-matrices with free entries on the diagonal

04/21/2021

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by   Eugene Kogan, et al.

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For an n × n matrix M with entries in ℤ_2 denote by R(M) the minimal rank of all the matrices obtained by changing some numbers on the main diagonal of M. We prove that for each non-negative integer k there is a polynomial in n algorithm deciding whether R(M) ≤ k (whose complexity may depend on k). We also give a polynomial in n algorithm computing a number m such that m/2 ≤ R(M) ≤ m. These results have applications to graph drawings on non-orientable surfaces.