Abstract
Given an n-vertex graph or digraph G, a spanning subgraph S is a k-spanner of G if for every u, v ∃ V(G), the distance from u to v in S is at most k times longer than the distance in G. This paper establishes some relationships between the connectivity and the existence of k-spanners with O(n) edges for graphs and digraphs. We give almost tight bounds of the connectivity of G which guarantees the existence of k-spanners with O(n) edges.
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© 1992 Springer-Verlag Berlin Heidelberg
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Ueno, S., Yamazaki, M., Kajitani, Y. (1992). Graph spanners and connectivity. In: Ibaraki, T., Inagaki, Y., Iwama, K., Nishizeki, T., Yamashita, M. (eds) Algorithms and Computation. ISAAC 1992. Lecture Notes in Computer Science, vol 650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56279-6_65
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DOI: https://doi.org/10.1007/3-540-56279-6_65
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