Hopcroft and Tarjan: deciding whether a network can lie in the plane

What changed

LOWPT-ordered DFSpath addition and linked stack constraints support linear planarity decision in the original list/RAM model.

Scientific scope

LOWPT-ordered DFSpath addition and linked stack constraints support linear planarity decision in the original list/RAM model. The original algorithm tests finite simple undirected graphs using adjacency lists, a bounded-word access model and biconnected-component reduction. Linear complexity does not mean reading a dense matrix in linear vertex time. The original test does not itself output a complete drawing/embedding. A bibliographically identified erratum has not been fully assessed, and pseudocode/transcription is not offered as certified runnable code.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

• John Hopcroft · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
• Robert Tarjan · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.

• Hopcroft and Tarjan: Efficient Planarity Testing(1974), original 549–568
• ACM: Efficient Planarity Testing publication metadata
• Mehlhorn/Mutzel: later detailed embedding phase, selected introduction only

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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