An Approximation Algorithm for the Tree t-Spanner Problem on Unweighted Graphs via Generalized Chordal Graphs.

A spanning tree T of a graph G is called a tree t- spanner of G if the distance between every pair of vertices in T is at most t times their distance in G. In this paper, we present an algorithm which constructs for an n-vertex m-edge unweighted graph G: For the latter result we use a new necessary condition for a graph to have a tree t-spanner: if a graph G has a tree t-spanner, then G admits a Robertson-Seymour's tree-decomposition with bags of radius at most ⌈ t/2⌉ and diameter at most t in G. [ABSTRACT FROM AUTHOR]