Convexity in graphs and hypergraphs
SIAM Journal on Algebraic and Discrete Methods
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
Dominating Cliques in Graphs with Hypertree Structures
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
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)
Spanners for bounded tree-length graphs
Theoretical Computer Science
The zoo of tree spanner problems
Discrete Applied Mathematics
Tree 3-spanners in 2-sep directed path graphs: Characterization, recognition, and construction
Discrete Applied Mathematics
Tree 3-spanners in 2-sep chordal graphs: Characterization and algorithms
Discrete Applied Mathematics
Complexity results for the spanning tree congestion problem
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Journal of Computer and System Sciences
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Distance approximating trees: complexity and algorithms
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Hi-index | 5.23 |
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 ≥ 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 ≥ 2 is even (respectively, t ≥ 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.