We give a simple proof for an important result of Edmonds, Lovász and Pulleyblank, stating that a brick has no non-trivial tight cuts. Our proof relies on some results on almost critical graphs. The introduction of these graphs is the second aim of the present paper.
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Szigeti, Z. Perfect Matchings Versus Odd Cuts. Combinatorica 22, 575–589 (2002). https://doi.org/10.1007/s00493-002-0008-6
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DOI: https://doi.org/10.1007/s00493-002-0008-6