Optimization problems in multiple subtree graphs

We study various optimization problems in t-subtree graphs  , the intersection graphs of tt-subtrees, where a tt-subtree is the union of tt disjoint subtrees of some tree. This graph class generalizes both the class of chordal graphs and the class of tt-interval graphs, a generalization of interval graphs that has recently been studied from a combinatorial optimization point of view. We present approximation algorithms for the Maximum Independent Set, Minimum Coloring, Minimum Vertex Cover, Minimum Dominating Set, and Maximum Clique problems.