On short cycles through prescribed vertices of a graph

F. Göring, J. Harant, E. Hexel, Zs Tuza

Research output: Contribution to journalConference article

4 Citations (Scopus)


For c≥2 and k≤min{c,3}, guaranteed upper bounds on the length of a shortest cycle through k prescribed vertices of a c-connected graphs were proved. Analogous results on planar graphs were also presented. A version of Menger's theorem and a structural lemma for c-connected graphs were proved. The upper bounds by constructing graphs having no cycles shorter than l containing the prescribed set of vertices and lower bounds by detecting large unavoidable substructures were established.

Original languageEnglish
Pages (from-to)67-74
Number of pages8
JournalDiscrete Mathematics
Issue number1-2
Publication statusPublished - Sep 6 2004
EventCycles and Colourings - Stara Lesna, Slovakia
Duration: Sep 9 2001Sep 14 2001


  • Graph
  • Prescribed vertices
  • Short cycle

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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