Minimal bricks have many vertices of small degree

We prove that every minimal brick on n vertices has at least n/9 vertices of degree at most 4.

[1]  Robin Thomas,et al.  Generating bricks , 2007, J. Comb. Theory, Ser. B.

[2]  László Lovász,et al.  Matching structure and the matching lattice , 1987, J. Comb. Theory, Ser. B.

[3]  László Lovász,et al.  Brick decompositions and the matching rank of graphs , 1982, Comb..

[4]  F. Rendl,et al.  Operations preserving the pfaffian property of a graph , 1991, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[5]  Robin Thomas,et al.  Minimal bricks , 2006, J. Comb. Theory, Ser. B.

[6]  Claudio L. Lucchesi,et al.  How to build a brick , 2006, Discret. Math..

[7]  Alexander Schrijver,et al.  Combinatorial optimization. Polyhedra and efficiency. , 2003 .

[8]  William J. Cook,et al.  Combinatorial optimization , 1997 .

[9]  A. Schrijver.  A Course in Combinatorial Optimization , 1990 .