On short cycles through prescribed vertices of a graph

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

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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
Volume286
Issue number1-2
DOIs
Publication statusPublished - Sep 6 2004

Fingerprint

Connected graph
Upper bound
Cycle
Substructure
Vertex of a graph
Planar graph
Lemma
Lower bound
Graph in graph theory
Theorem

Keywords

  • Graph
  • Prescribed vertices
  • Short cycle

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

On short cycles through prescribed vertices of a graph. / Göring, F.; Harant, J.; Hexel, E.; Tuza, Z.

In: Discrete Mathematics, Vol. 286, No. 1-2, 06.09.2004, p. 67-74.

Research output: Contribution to journalArticle

Göring, F. ; Harant, J. ; Hexel, E. ; Tuza, Z. / On short cycles through prescribed vertices of a graph. In: Discrete Mathematics. 2004 ; Vol. 286, No. 1-2. pp. 67-74.
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