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Dense $2$-connected planar graphs and the planar Tur\'{a}n number of $2C_k$

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arxiv 2503.09367 v3 pith:27VBDOUV submitted 2025-03-12 math.CO

classification math.CO
keywords planarconnecteddensegraphgraphsnumberresultaddressing
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abstract

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 Tu\'{a}n number of $2C_k$ is $\left[3-\Theta(k^{\log_23})^{-1}\right]n$ when $k\geq 5$.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Planar Tur\'{a}n numbers of three configurations

    math.CO 2025-09 conditional novelty 6.0 of 10

    Exact planar Turán numbers are established for K1+(P2∪P3), a combined C3/Θ4 configuration, and the disjoint union of C3 and Θ4, with extremal graph characterizations.

  2. Planar Tur\'an number of disjoint union of $C_3$ and $C_5$

    math.CO 2025-07 conditional novelty 6.0 of 10

    For n ≥ 295660, the planar Turán number of C3∪C5 is floor((8n-13)/3), and the unique extremal planar graph is described.

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