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This is a Quantitative Study study.

On k-planar Graphs without Short Cycles

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Short cycles can significantly affect edge density in k-planar graphs, particularly at lower values of k.
Lower and upper bounds on the number of edges are established for k-planar graphs on n vertices, relevant for k values including 1, 2, and 3.
The findings involve methods like the discharging method and leverage known density formulas to reach conclusions.
These insights are crucial for understanding the structural properties of k-planar graphs as k increases beyond four.

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This study presents bounds on edge density in k-planar graphs with forbidden cycles, indicating key structural implications.

Bekos et al. (2025) studied this question.

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