Abstract
In this paper we study collective additive tree spanners for families of graphs that either contain or are contained in AT-free graphs. We say that a graph G=(V,E) admits a system of μ collective additive tree r -spanners if there is a system \({\cal T}(G)\) of at most μ spanning trees of G such that for any two vertices x,y of G a spanning tree \(T\in {\cal T}(G)\) exists such that d T (x,y)≤ d G (x,y)+r. Among other results, we show that AT-free graphs have a system of two collective additive tree 2-spanners (whereas there are trapezoid graphs that do not admit any additive tree 2-spanner). Furthermore, based on this collection of trees, we derive a compact and efficient routing scheme for those graphs. Also, any DSP-graph (there exists a dominating shortest path) admits one additive tree 4-spanner, a system of two collective additive tree 3-spanners and a system of five collective additive tree 2-spanners.
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Dragan, F.F., Yan, C., Corneil, D.G. (2004). Collective Tree Spanners and Routing in AT-free Related Graphs. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2004. Lecture Notes in Computer Science, vol 3353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30559-0_6
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DOI: https://doi.org/10.1007/978-3-540-30559-0_6
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