Publication Date
August 2025
Abstract
A graph $G$ is $k$-degenerate if each subgraph has minimum degree
at most $k$. The degeneracy\textbf{ }$D\left(G\right)$ is the smallest
$k$ such that $G$ is $k$-degenerate. We determine the truth values
of four statements (using different quantifiers) about when a planar
graph $G$ with degeneracy $k$ has a triangulation with degeneracy
$l$. We characterize which 3-connected planar graphs can only be
triangulated to degeneracy 3. Then we consider analogous questions
for maximal planar bipartite graphs. We prove some structural results
on these graphs, including results on decomposition of planar graphs
into various types of bipartite graphs.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Bickle, Allan
(2025)
"Degeneracies of Triangulated Graphs,"
Theory and Applications of Graphs: Vol. 12:
Iss.
2, Article 1.
DOI: 10.20429/tag.2025.120201
Available at:
https://digitalcommons.georgiasouthern.edu/tag/vol12/iss2/1
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