Transversals of longest cycles in partial k-trees and chordal graphs

Let (Formula presented.) be the minimum cardinality of a set of vertices that intersects every longest cycle of a 2-connected graph (Formula presented.). We show that (Formula presented.) if (Formula presented.) is a partial (Formula presented.) -tree and that (Formula presented.) if (Formula presented.) is chordal, where (Formula presented.) is the cardinality of a maximum clique in (Formula presented.). Those results imply that all longest cycles intersect in 2-connected series-parallel graphs and in 3-trees.