Strengthens the solvability of Mx=diag(M) for symmetric M over F2 to a parity rigidity theorem diag(M)^T x ≡ rank(M) mod 2, with rank-update formulas and tree recursions for generalized odd-domination.
Batal, Parity of an odd dominating set,Commun
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Diagonal parity and loop toggling for symmetric matrices over $\mathbb F_2$
Strengthens the solvability of Mx=diag(M) for symmetric M over F2 to a parity rigidity theorem diag(M)^T x ≡ rank(M) mod 2, with rank-update formulas and tree recursions for generalized odd-domination.