Transversals of longest cycles in partial k-trees and chordal graphs

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Abstract

Let (Formula presented.) be the minimum cardinality of a set of vertices that intersects every longest cycle of a 2-connected graph (Formula presented.). We show that (Formula presented.) if (Formula presented.) is a partial (Formula presented.) -tree and that (Formula presented.) if (Formula presented.) is chordal, where (Formula presented.) is the cardinality of a maximum clique in (Formula presented.). Those results imply that all longest cycles intersect in 2-connected series-parallel graphs and in 3-trees.

Original languageEnglish
Pages (from-to)589-603
Number of pages15
JournalJournal of Graph Theory
Volume98
Issue number4
DOIs
StatePublished - Dec 2021

Keywords

  • chordal graph
  • longest cycle
  • partial k-tree
  • transversal
  • treewidth

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