# Tree 3-spanners in 2-sep chordal graphs: Characterization and algorithms

Panda, BS and Das, Anita (2010) Tree 3-spanners in 2-sep chordal graphs: Characterization and algorithms. In: Discrete Applied Mathematics, 158 (17). pp. 1913-1935.

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Official URL: http://dx.doi.org/10.1016/j.dam.2010.08.015

## Abstract

A spanning tree T of a graph G is said to be a tree t-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 tree t-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. (C) 2010 Elsevier B.V. All rights reserved.

Item Type: Journal Article Copyright of this article belongs to Elsevier Science B.V. Tree spanner; Distance in graphs; Graph algorithms; 2-sep Chordal graphs Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation) 29 Nov 2010 12:08 29 Nov 2010 12:08 http://eprints.iisc.ernet.in/id/eprint/33974