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arXiv · 2501.02400

Skewness, crossing number and Euler's bound for graphs on surfaces

Paul C. Kainen
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Abstract

For every connected graph $G$ and surface $S$, we consider the well-known string of inequalities $δ_S(G) \leq μ_S(G) \leq ν_S(G)$, where $μ$ and $ν$ denote skewness and crossing number and $δ$ is the Euler-formula lower bound. Recent developments are surveyed; new results are given for the ``folded'' cube including its genus.

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Paul C. Kainen. 2025-01-04. Skewness, crossing number and Euler's bound for graphs on surfaces. https://arxiv.org/abs/2501.02400

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