Lines in the plane and decompositions of graphs

  • Martin Aigner
  • Günter M. Ziegler


Perhaps the best-known problem on configurations of lines was raised by Sylvester in 1893 in a column of mathematical problems.


Complete Bipartite Graph Partite Graph Real Plane Bipartite Subgraph Fano Plane 
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    H. S. M. coxeter: A problem of collinear points,Amer. Math. Monthly 55 (1948), 26-28 (contains Kelly’s proof).Google Scholar
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    P. Erdős:Problem 4065 — Three point collinearity,Amer. Math. Monthly 51 (1944), 169-171 (contains Gallai’s proof).Google Scholar
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    R. L. Graham & H. O. Pollak: On the addressing problem for loop switching, Bell System Tech. J. 50 (1971), 2495 - 2519.MathSciNetMATHGoogle Scholar
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    J. J. Sylvester: Mathematical Question 11851, The Educational Times 46 (1893), 156.Google Scholar
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    H. TVERBERG: On the decomposition of K, into complete bipartite graphs, J. Graph Theory 6 (1982), 493 - 494.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Martin Aigner
    • 1
  • Günter M. Ziegler
    • 2
  1. 1.Institut für Mathematik II (WE2)Freie Universität BerlinBerlinGermany
  2. 2.Fachbereich Mathematik, MA 7-1Technische Universität BerlinBerlinGermany

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