The Cubic Vertices of Minimal Bricks

2013/06/20 by Fenggen Lin, Lianzhu Zhang, Fuliang Lu

paper · doi:10.1002/jgt.21747

Abstract

Abstract 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.

Related

• On a Norine–Thomas conjecture concerning minimal bricks
• Cubic vertices of minimal bicritical graphs
• Minimal bricks have many vertices of small degree
• Cubic bricks that every b-invariant edge is forcing
• Generating Near-Bipartite Bricks