Minimal bricks
arXiv:1907.00305 · doi:10.1016/j.jctb.2005.10.005
Abstract
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>4, 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.
10 pages, 2 figures. This version fixes an error kindly pointed to us by P. A. Fabres, N. Kothari and M. H. de Carvalho