Dual Circumference and Collinear Sets

نویسندگان

چکیده

We show that, if an n-vertex triangulation G of maximum degree $$\Delta $$ has a dual that contains cycle length $$\ell , then non-crossing straight-line drawing in which some set, called collinear $$\Omega (\ell /\Delta ^4)$$ vertices lie on line. Using the current lower bounds longest cycles cubic 3-connected graphs, this implies every planar graph set size (n^{0.8}/\Delta .

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ژورنال

عنوان ژورنال: Discrete and Computational Geometry

سال: 2022

ISSN: ['1432-0444', '0179-5376']

DOI: https://doi.org/10.1007/s00454-022-00418-4