Graph spanners and connectivity

  • Shuichi Ueno
  • Michihiro Yamazaki
  • Yoji Kajitani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 650)


Given an n-vertex graph or digraph G, a spanning subgraph S is a k-spanner of G if for every u, vV(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.


Polynomial Time Complete Graph Weighted Graph Chordal Graph Tight Bound 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    I. Althöfer. On optimal realizations of finite metric spaces by graphs. Discrete and Computational Geometry, 3:103–122, 1988.Google Scholar
  2. [2]
    I. Althöfer, G. Das, D. Dobkin, and D. Joseph. Generating sparse spanners for weighted graphs. In LNCS 447, pages 26–37, 1990.Google Scholar
  3. [3]
    B. Awerbuch. Complexity of network synchronization. J. ACM, 32:804–823, 1985.Google Scholar
  4. [4]
    B. Awerbuch, A. Bar-Noy, N. Linial, and D. Peleg. Compact distributed data structures for adaptive routing. In STOC, pages 479–489, 1989.Google Scholar
  5. [5]
    B. Awerbuch, O. Goldreich, D. Peleg, and R. Vainish. A tradeoff between information and communication in broadcast protocols. In LNCS 319, pages 369–379, 1988.Google Scholar
  6. [6]
    B. Awerbuch and D. Peleg. Sparse partitions. In FOCS, pages 503–513, 1990.Google Scholar
  7. [7]
    Bandelt and Dress. Reconstructing the shape of a tree from observed dissimilarity data. Advances in Appl. Maths., 7:309–343, 1986.CrossRefGoogle Scholar
  8. [8]
    B. Bollobás. Extremal Graph Theory. Academic Press, 1978.Google Scholar
  9. [9]
    L. P. Chew. There are planar graphs almost as good as the complete graph. J. Comput. System Sci., 39:205–219, 1989.CrossRefGoogle Scholar
  10. [10]
    G. Das and D. Joseph. Which triangulations approximate the complete graph? In LNCS 401, pages 168–192, 1989.Google Scholar
  11. [11]
    D. P. Dobkin, S. J. Friedman, and K. J. Supowit. Delaunay graphs are almost as good as complete graphs. In FOCS, pages 20–26, 1987.Google Scholar
  12. [12]
    J. M. Keil. Approximating the complete euclidean graph. In LNCS 318, pages 208–213, 1988.Google Scholar
  13. [13]
    J. M. Keil and C. A. Gutwin. Classes of graphs which approximate the complete euclidean graph. Discrete Comput. Geom., 7:13–28, 1992.Google Scholar
  14. [14]
    C. Levcopoulos and A. Lingas. There are planar graphs almost as good as the complete graphs and as short as minimum spanning trees. In LNCS 401, pages 9–13, 1989.Google Scholar
  15. [15]
    W. Mader. Existenz n-fachen zusammenhÄngenden teilgraphen in graphen genügend grosser kantendichte. Abh. Math. Sem. Univ. Hamburg, 37:86–97, 1972.Google Scholar
  16. [16]
    D. Peleg and A. A. SchÄffer. Graph spanners. J. Graph Theory, 13:99–116, 1989.Google Scholar
  17. [17]
    D. Peleg and J. D. Ullman. An optimal synchronizer for the hypercube. SIAM J. Comput., 18:740–747, 1989.CrossRefGoogle Scholar
  18. [18]
    D. Peleg and E. Upfal. A tradeoff between space and efficiency for routing tables. In STOC, pages 43–52, 1988.Google Scholar
  19. [19]
    C. Thomassen. Paths, cycles and subdivisions. In L. W. Beineke and R. J. Wilson, editors, Selected Topics in Graph Theory III, Academic Press, 1988.Google Scholar
  20. [20]
    P. M. Vaidya. A sparse graph almost as good as the complete graph on points in k dimensions. Discrete Comput. Geom., 6:369–381, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Shuichi Ueno
    • 1
  • Michihiro Yamazaki
    • 1
  • Yoji Kajitani
    • 1
    • 2
  1. 1.Department of Electrical and Electronic EngineeringTokyo Institute of TechnologyTokyoJapan
  2. 2.School of Information ScienceIshikawaJapan

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