The Cubic Vertices of Minimal Bricks


  • Contract grant sponsor: NSFC; contract grant numbers: 10831001, 11171279, 11226033, and 11226288; contract grant sponsor: Fuzhou University; contract grant numbers: 022458 and 600628.


A graph is a brick if it is 3-connected and bicritical. A brick is minimal if for every edge, the deletion of it results in a graph that is not a brick. In this article, we prove that every minimal brick has at least four cubic vertices.