Minimal bricks. (English) Zbl 1092.05056
Summary: 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 \(n\geq 5\), 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.
MSC:
| 05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |
References:
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