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Alpha-balanced graphs and matrices and GF(3)-representability of matroids. (English) Zbl 0478.05026

MSC:
05B35 Combinatorial aspects of matroids and geometric lattices
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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[1] Berge, C, ()
[2] Berge, C, Balanced matrices, Math. programming, 2, 19-31, (1972) · Zbl 0247.05126
[3] Bixby, R.E, On Reid’s characterization of the ternary matroids, J. combin. theory ser. B, 26, 174-204, (1979) · Zbl 0405.05022
[4] Brylawski, T.H; Lucas, D, Uniquely representable combinatorial geometrics, () · Zbl 0392.51007
[5] Camion, P, Characterization of totally unimodular matrices, (), 1068-1073 · Zbl 0134.25201
[6] Fulkerson, D.R; Hoffman, A.J; Oppenheim, R, On balanced matrices, Math. programming stud., 1, 120-132, (1974) · Zbl 0357.90038
[7] Seymour, P.D, Matroid representation over GF(3), J. combin. theory ser. B, 26, 159-173, (1979) · Zbl 0443.05029
[8] Seymour, P.D, Decomposition of regular matroids, J. combin. theory ser. B, 28, 305-359, (1980) · Zbl 0443.05027
[9] Truemper, K; Chandrasekaran, R, Local unimodularity of matrix-vector pairs, Linear algebra appl., 22, 65-78, (1978) · Zbl 0395.90053
[10] Truemper, K, Complement total unimodularity, Linear algebra appl., 30, 77-92, (1980) · Zbl 0442.15010
[11] Truemper, K, (), Working Paper
[12] Tutte, W.T, A homotopy theorem for matroids, I, II, Trans. amer. math. soc., 88, 144-174, (1958) · Zbl 0081.17301
[13] Tutte, W.T, Lectures on matroids, J. res. nat. bur. standards sect. B, 69, 1-47, (1965) · Zbl 0151.33801
[14] Tutte, W.T, ()
[15] Welsh, D.J.A, ()
[16] Zaslavsky, T, Characterizations of signed graphs, J. graph theory, 5, 401-406, (1981) · Zbl 0471.05035
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