Two graph classes are presented; the first one (k-ribbon) generalizes the path graph and the second one (k-fan) generalizes the fan graph. We prove that they are subclasses of chordal graphs and so they share the same structural properties of this class. The solution of two problems are presented: the determination of the subchromatic number and the determination of the toughness. It is shown that the elements of the new classes establish bounds for the toughness of k-path graphs.
k-path graphs; k-ribbon graphs; k-fan graphs; subcoloring; toughness
