Ear Decompositions of Matching Covered Graphs

@article{Carvalho1999EarDO,
  title={Ear Decompositions of Matching Covered Graphs},
  author={Marcelo H. de Carvalho and Claudio L. Lucchesi and Uppaluri S. R. Murty},
  journal={Combinatorica},
  year={1999},
  volume={19},
  pages={151-174}
}
G different from and has at least Δ edge-disjoint removable ears, where Δ is the maximum degree of G. This shows that any matching covered graph G has at least Δ! different ear decompositions, and thus is a generalization of the fundamental theorem of Lovász and Plummer establishing the existence of ear decompositions. We also show that every brick G different from and has Δ− 2 edges, each of which is a removable edge in G, that is, an edge whose deletion from G results in a matching covered… 
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