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arXiv · 1912.12230

Transversals of Longest Cycles in Partial $k$-Trees and Chordal Graphs

Juan Gutiérrez
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Abstract

Let $lct(G)$ be the minimum cardinality of a set of vertices that intersects every longest cycle of a 2-connected graph $G$. We show that $lct(G)\leq k-1$ if $G$ is a partial $k$-tree and that $lct(G)\leq \max \{1, {\omega(G){-}3}\}$ if $G$ is chordal, where $\omega(G)$ is the cardinality of a maximum clique in $G$. Those results imply that all longest cycles intersect in 2-connected series parallel graphs and in 3-trees.

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Juan Gutiérrez. 2019-12-27. Transversals of Longest Cycles in Partial $k$-Trees and Chordal Graphs. https://arxiv.org/abs/1912.12230

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