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arXiv · 1712.07086

Transversals of Longest Paths

Márcia R. Cerioli·Cristina G. Fernandes·Renzo Gómez·Juan Gutiérrez·Paloma T. Lima
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Abstract

Let $\lpt(G)$ be the minimum cardinality of a set of vertices that intersects all longest paths in a graph $G$. Let $\omega(G)$ be the size of a maximum clique in $G$, and $\tw(G)$ be the treewidth of $G$. We prove that $ \lpt(G) \leq \max\{1,\omega(G)-2\}$ when $G$ is a connected chordal graph; that $\lpt(G) =1$ when $G$ is a connected bipartite permutation graph or a connected full substar graph; and that $\lpt(G) \leq \tw(G)$ for any connected graph $G$.

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Márcia R. Cerioli, Cristina G. Fernandes, Renzo Gómez, Juan Gutiérrez, Paloma T. Lima. 2017-12-19. Transversals of Longest Paths. https://arxiv.org/abs/1712.07086

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