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October 3, 2025Open Access

Planar induced paths via a decomposition into non-crossing ordered graphs

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Induced paths in planar graphs are tightly bounded, showing computational significance in graph theory.
The maximum induced path size is shown to be Θ(log n/log log n) in planar graphs with paths of size n.
Edge partitions in graphs ordered along Hamiltonian paths offer critical insight into induced path sizes.
The approach establishes both upper and lower bounds for induced paths, enhancing understanding of graph structures.

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This paper demonstrates the bounds on induced paths in planar graphs, indicating potential in graph theory.

Duron et al. (2025) studied this question.

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