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

  • Juan Gutiérrez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Ciência da ComputaçãoUniversidade de São PauloSão PauloBrazil

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