Transversals of Longest Paths

12/19/2017

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by   Márcia R. Cerioli, et al.

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