Minimal bricks have many vertices of small degree
Henning Bruhn, Maya Stein

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.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Advanced Topology and Set Theory
