Matching structure and the matching lattice
Journal of Combinatorial Theory Series B
Pfaffian orientations 0-1 permanents, and even cycles in directed graphs
Discrete Applied Mathematics - Combinatorics and complexity
Minimal bricks have many vertices of small degree
European Journal of Combinatorics
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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.