Reconstructing the shape of a tree from observed dissimilarity data
Advances in Applied Mathematics
Tree spanners: spanning trees that approximate distances
Tree spanners: spanning trees that approximate distances
SIAM Journal on Discrete Mathematics
Tree 3-spanners on interval, permutation and regular bipartite graphs
Information Processing Letters
Restrictions of minimum spanner problems
Information and Computation
Graph classes: a survey
Distance approximating trees for chordal and dually chordal graphs
Journal of Algorithms
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Tree spanners in planar graphs
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Distance Approximating Spanning Trees
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
A Linear-Time Algorithm for Finding a Central Vertex of a Chordal Graph
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Additive sparse spanners for graphs with bounded length of largest induced cycle
Theoretical Computer Science
Additive spanners for k-chordal graphs
CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
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A tree t-spanner T in a graph G is a spanning tree of G such that the distance in T between every pair of vertices is at most t times their distance in G. The TREE t-SPANNER problem asks whether a graph admits a tree t-spanner, given t. We substantially strengthen the hardness result of Cai and Corneil [SIAM J. Discrete Math. 8 (1995) 359- 387] by showing that, for any t 驴 4, TREE t-SPANNER is NP-complete even on chordal graphs of diameter at most t + 1 (if t is even), respectively, at most t + 2 (if t is odd).Then we point out that every chordal graph of diameter at most t - 1 (respectively, t - 2) admits a tree t-spanner whenever t 驴 2 is even (respectively, t 驴 3 is odd), and such a tree spanner can be constructed in linear time.The complexity status of TREE 3-SPANNER still remains open for chordal graphs, even on the subclass of undirected path graphs that are strongly chordal as well. For other important subclasses of chordal graphs, such as very strongly chordal graphs (containing all interval graphs), 1-split graphs (containing all split graphs) and chordal graphs of diameter at most 2, we are able to decide Tree 3-Spanner efficiently.