Sur le problème des courbes gauches en topologie

Kuratowski, K. (1930). Sur le problème des courbes gauches en topologie. Fundamenta Mathematicae, 15, 271-283.

Type

Journal article

Intellectual base

Primary research

Year

1930

Volume

15

Pages

271-283

Link

https://eudml.org/doc/212352

Cited from

mathematics

Cited by

2 citations across 2 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Embeddability
  • The tripartite skeleton recurs across genuinely distinct substrates. Graph theory supplies the canonical case: planarity asks whether a graph embeds in the plane with no edge crossings, with Kuratowski's forbidden-minor theorem as the structural characterisation and linear-time planarity testing as the algorithmic answer; higher-genus embeddability generalises this to surfaces.

Domain-specific

• Planarity
  • The property has a sharp combinatorial characterization given by Kuratowski's theorem (1930): a graph is planar if and only if it contains no subdivision of K₅ (the complete graph on five vertices) or K₃,₃ (the complete bipartite graph on three plus three vertices)

    This sourceProves that a graph-like curve is planar exactly when it contains no homeomorph (subdivision) of K5 or K3,3.

    SupportedVerified against the source

    Read by an automated reader; not a human review. How support was checked

Verification

Does it exist? Not checked yet. This entry carries no identifier to resolve. It was extracted from the citation as written in the article, normalized, and deduplicated against the rest of the registry.

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