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Latin American Symposium on Theoretical Informatics

LATIN 2018: LATIN 2018: Theoretical Informatics pp 558–571Cite as

Transversals of Longest Cycles in Chordal and Bounded Tree-Width Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10807))

Abstract

Let \(\mathrm {lct}(G)\) be the minimum size of a set of vertices that intersects every longest cycle of a 2-connected graph G. Let \(\mathrm {tw}(G)\) be the tree-width of G and \(\omega (G)\) be the size of a maximum clique in G. We show that \(\mathrm {lct}(G)\le \mathrm {tw}(G)-1\) for every G, and that \(\mathrm {lct}(G)\le \max \{1, {\omega (G){-}3}\}\) if G is chordal. Those results imply as corollaries that all longest cycles intersect in 2-connected series-parallel graphs and in 3-trees. We also strengthen the latter result and show that all longest cycles intersect in 2-connected graphs of tree-width at most 3, also known as partial 3-trees.

J. Gutiérrez—Research supported by FAPESP (Proc. 2015/08538-5).

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Authors and Affiliations

  1. Departamento de Ciência da Computação, Universidade de São Paulo, Rua do Matão 1010, São Paulo, SP, 05508–090, Brazil

    Juan Gutiérrez

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  1. Juan Gutiérrez
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Correspondence to Juan Gutiérrez .

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Editors and Affiliations

  1. Stony Brook University, Stony Brook, New York, USA

    Michael A. Bender

  2. Rutgers University, New Brunswick, New Jersey, USA

    Martín Farach-Colton

  3. Pace University, New York, New York, USA

    Miguel A. Mosteiro

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Gutiérrez, J. (2018). Transversals of Longest Cycles in Chordal and Bounded Tree-Width Graphs. In: Bender, M., Farach-Colton, M., Mosteiro, M. (eds) LATIN 2018: Theoretical Informatics. LATIN 2018. Lecture Notes in Computer Science(), vol 10807. Springer, Cham. https://doi.org/10.1007/978-3-319-77404-6_41

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  • DOI: https://doi.org/10.1007/978-3-319-77404-6_41

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-77403-9

  • Online ISBN: 978-3-319-77404-6

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