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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.09367 |
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Table of Contents:
- Shi, Walsh and Yu demonstrated that any dense planar graph with certain property (known as circuit graph) contains a large near-triangulation. We extend the result to $2$-connected plane graphs, thereby addressing a question posed by them. Using the result, we prove that the planar Tuán number of $2C_k$ is $\left[3-Θ(k^{\log_23})^{-1}\right]n$ when $k\geq 5$.