Abstract
In this note we show that, for each chordal graph G, there is a tree T such that T is a spanning tree of the square G 2 of G and, for every two vertices, the distance between them in T is not larger than the distance in G plus two. Moreover, we prove that, if G is a strongly chordal graph or even a dually chordal graph, then there exists a spanning tree T of G which is an additive 3-spanner as well as a multiplicative 4-spanner of G. In all cases the tree T can be computed in linear time.
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Brandstädt, A., Chepoi, V., Dragan, F. (1997). Distance approximating trees for chordal and dually chordal graphs. In: Burkard, R., Woeginger, G. (eds) Algorithms — ESA '97. ESA 1997. Lecture Notes in Computer Science, vol 1284. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63397-9_7
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DOI: https://doi.org/10.1007/3-540-63397-9_7
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