Abstract
We demonstrate that two key theorems of Amaldi et al. (Math Methods Oper Res 69:205–223, 2009), which they presented with rather complicated proofs, can be more easily and cleanly established using a simple and classical property of binary matroids. Besides a simpler proof, we see that both of these key results are manifestations of the same essential property.
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References
Amaldi E, Liberti L, Maffioli F, Maculan N (2009) Edge-swapping algorithms for the minimum fundamental cycle basis problem. Math Methods Oper Res 69: 205–223
Oxley J (1992) Matroid theory. Oxford University Press, New York
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Lee, J., Liberti, L. A matroid view of key theorems for edge-swapping algorithms. Math Meth Oper Res 76, 125–127 (2012). https://doi.org/10.1007/s00186-012-0392-7
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DOI: https://doi.org/10.1007/s00186-012-0392-7