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

Juan Gutiérrez

doi:10.1002/jgt.22714

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

Juan Gutiérrez

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 language	English
Pages (from-to)	589-603
Number of pages	15
Journal	Journal of Graph Theory
Volume	98
Issue number	4
DOIs	https://doi.org/10.1002/jgt.22714
State	Published - Dec 2021

Keywords

chordal graph
longest cycle
partial k-tree
transversal
treewidth

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10.1002/jgt.22714

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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.",

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AB - 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.

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KW - longest cycle

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KW - transversal

KW - treewidth

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

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Keywords

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