Minimal bricks have many vertices of small degree

TL;DR

This paper proves that in any minimal brick graph with n vertices, at least one-ninth of the vertices have degree at most 4, revealing a structural property of these graphs.

Contribution

The paper establishes a new lower bound on the number of vertices with small degree in minimal brick graphs, advancing understanding of their structure.

Findings

At least n/9 vertices have degree ≤ 4 in minimal bricks.

Provides a structural bound on minimal brick graphs.

Enhances theoretical understanding of graph degree distributions.

Abstract

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