Kuratowski Chains

Neil Robertson, Paul Seymour, Robin Thomas

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We prove that if H and H’ are subgraphs of a graph G, and both are isomorphic to subdivisions of K5 or K3, 3, then the following are equivalent: (i) there is a sequence H = H1, H2, ⋯, Hk = H’ of subgraphs of G, each isomorphic to a subdivision of K5 or K3, 3 and each differing only a “small amounty” from its predecessor; (ii) H and H’ are not “separated” in G by a vertex separation of order ≤ 3. This is a lemma for use in a future paper concerning linkless embeddings of graphs in 3-space.

Original languageEnglish (US)
Pages (from-to)127-154
Number of pages28
JournalJournal of Combinatorial Theory, Series B
Issue number2
StatePublished - Jul 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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