Minimal bricks

@article{Norine2006MinimalB,
  title={Minimal bricks},
  author={Serguei Norine and Robin Thomas},
  journal={J. Comb. Theory, Ser. B},
  year={2006},
  volume={96},
  pages={505-513}
}
A brick is a 3-connected graph such that the graph obtained from it by deleting any two distinct vertices has a perfect matching. A brick is minimal if for every edge e the deletion of e results in a graph that is not a brick. We prove a generation theorem for minimal bricks and two corollaries: (1) for n ≥ 5, every minimal brick on 2n vertices has at most 5n − 7 edges, and (2) every minimal brick has at least three vertices of degree three. 

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