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On Mighton’s characterization of graphic matroids. (English) Zbl 1203.05030
Summary: J. Mighton [“A new characterization of graphic matroids,” J. Comb. Theory, Ser. B 98, No. 6, 1253–1258 (2008; Zbl 1170.05020)] recently gave a new characterization of graphic matroids. This note combines Mighton’s approach with a result of W.H. Cunningham [“Separating cocircuits in binary matroids,” Linear Algebra Appl. 43, 69–86 (1982; Zbl 0487.05015)] to provide a shorter, more direct proof of Mighton’s result.

05B35 Combinatorial aspects of matroids and geometric lattices
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[1] Bixby, R.E., Bridges in general matroids, (1979), Bell Laboratories Technical Memorandum
[2] Bixby, R.E.; Cunningham, W.H., Matroids, graphs, and 3-connectivity, (), 91-103
[3] Bixby, R.E.; Cunningham, W.H., Converting linear programs to network problems, Math. oper. res., 5, 321-357, (1980) · Zbl 0442.90095
[4] Cunningham, W.H., Separating cocircuits in binary matroids, Linear algebra appl., 43, 69-86, (1982) · Zbl 0487.05015
[5] Mighton, J., A new characterization of graphic matroids, J. combin. theory ser. B, 98, 1253-1258, (2008) · Zbl 1170.05020
[6] Oxley, J.G., Matroid theory, (1992), Oxford University Press Oxford · Zbl 0784.05002
[7] Tutte, W.T., An algorithm for determining whether a given binary matroid is graphic, Proc. amer. math. soc., 11, 905-917, (1960) · Zbl 0097.38905
[8] Tutte, W.T., On even matroids, J. research national bureau standards sect. B, 71, 213-214, (1967) · Zbl 0165.26801
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