Transversals of Longest Paths.

Let lpt( G ) be the minimum cardinality of a set of vertices that intersects all longest paths in a connected graph G . We show that, if G is a chordal graph, then lpt ( G ) ≤ max ⁡ { 1 , ω ( G ) − 2 } , where ω ( G ) is the size of a largest clique in G ; that lpt ( G ) ≤ tw ( G ) , where tw ( G ) is the treewidth of G ; and that lpt ( G ) = 1 if G is a bipartite permutation graph or a full substar graph. [ABSTRACT FROM AUTHOR]