Reconstructing the shape of a tree from observed dissimilarity data
Advances in Applied Mathematics
An optimal synchronizer for the hypercube
PODC '87 Proceedings of the sixth annual ACM Symposium on Principles of distributed computing
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Tree spanners: spanning trees that approximate distances
Tree spanners: spanning trees that approximate distances
SIAM Journal on Discrete Mathematics
Intersection graphs of vertex disjoint paths in a tree
Discrete Mathematics
Tree 3-spanners on interval, permutation and regular bipartite graphs
Information Processing Letters
Restrictions of minimum spanner problems
Information and Computation
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
SIAM Journal on Discrete Mathematics
Tree spanners on chordal graphs: complexity and algorithms
Theoretical Computer Science
Optimal simulations of tree machines
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Tree 3-spanners in 2-sep directed path graphs: Characterization, recognition, and construction
Discrete Applied Mathematics
| Hi-index | 0.04 |
A spanning tree T of a graph G is said to be a treet-spanner if the distance between any two vertices in T is at most t times their distance in G. A graph that has a tree t-spanner is called a treet-spanner admissible graph. The problem of deciding whether a graph is tree t-spanner admissible is NP-complete for any fixed t=4 and is linearly solvable for t@?2. The case t=3 still remains open. A chordal graph is called a 2-sep chordal graph if all of its minimal a-b vertex separators for every pair of non-adjacent vertices a and b are of size two. It is known that not all 2-sep chordal graphs admit tree 3-spanners. This paper presents a structural characterization and a linear time recognition algorithm of tree 3-spanner admissible 2-sep chordal graphs. Finally, a linear time algorithm to construct a tree 3-spanner of a tree 3-spanner admissible 2-sep chordal graph is proposed.