Abstract
In this paper we study the existence of a small set \(\mathcal{T}\) of spanning trees that collectively “1-span” an interval graph G. In particular, for any pair of vertices u,v we require a tree \(T \in \mathcal{T}\)such that the distance between u and v in T is at most one more than their distance in G. We show that:
– there is no constant size set of collective tree 1-spanners for interval graphs (even unit interval graphs),
– interval graph G has a set of collective tree 1-spanners of size O(log D), where D is the diameter of G,
– interval graphs have a 1-spanner with fewer than 2n – 2 edges.
Furthermore, at the end of the paper we state other results on collective tree c-spanners for c > 1 and other more general graph classes.
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Corneil, D.G., Dragan, F.F., Köhler, E., Yan, C. (2005). Collective Tree 1-Spanners for Interval Graphs. In: Kratsch, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2005. Lecture Notes in Computer Science, vol 3787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11604686_14
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DOI: https://doi.org/10.1007/11604686_14
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