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Transversals of Longest Paths (1712.07086v1)
Published 19 Dec 2017 in cs.DM and math.CO
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 $G$.