WRSWorld Research StateContribute
WORLD RESEARCH STATE

Kuratowski: characterization of planar graphs

Contribution grade

Combinatorics and discrete mathematics · THEOREM

Reference score220,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

Characterized finite planar graphs by absence of K5 and K3,3 subdivisions.

Scientific scope

The record is Kuratowski's sole-author 1930 Fundamenta Mathematicae paper. It does not absorb Wagner's minor theorem, later algorithms, infinite-graph extensions or Kuratowski's earlier closure axioms.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The record is Kuratowski's sole-author 1930 Fundamenta Mathematicae paper. It does not absorb Wagner's minor theorem, later algorithms, infinite-graph extensions or Kuratowski's earlier closure axioms.

Contributors

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

Full scientific record · Browse contribution grades · Request a correction