Tree Spanners for Bipartite Graphs and Probe Interval Graphs

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Tree Spanners for Bipartite Graphs and Probe Interval Graphs
A tree t-spanner T in a graph G is a spanning tree of G such that the distance between every pair of vertices in T 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 first substantially strengthen the known results for bipartite graphs. We prove that the tree t-spanner problem is NP-complete even for chordal bipartite graphs for t ≥ 5, and every bipartite ATE–free graph has a tree 3-spanner, which can be found in linear time. The best known before results were NP-completeness for general bipartite graphs, and that every convex graph has a tree 3-spanner. We next focus on the tree t-spanner problem for probe interval graphs and related graph classes. The graph classes were introduced to deal with the physical mapping of DNA. From a graph theoretical point of view, the classes are natural generalizations of interval graphs. We show that these classes are tree 7-spanner admissible, and a tree 7-spanner can be c...
Andreas Brandstädt, Feodor F. Dragan, Ho&agra
Added 08 Dec 2010
Updated 08 Dec 2010
Type Journal
Year 2007
Authors Andreas Brandstädt, Feodor F. Dragan, Hoàng-Oanh Le, Van Bang Le, Ryuhei Uehara
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