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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.

MSC:
05B35 Combinatorial aspects of matroids and geometric lattices
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References:
[1] Bixby, R.E., Bridges in general matroids, (1979), Bell Laboratories Technical Memorandum
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[4] Cunningham, W.H., Separating cocircuits in binary matroids, Linear algebra appl., 43, 69-86, (1982) · Zbl 0487.05015
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