Combinatorica

, Volume 19, Issue 4, pp 473–486 | Cite as

Exact Bounds for Judicious Partitions of Graphs

  • B. Bollobás
  • A. D. Scott
Original Paper

has a bipartite subgraph of size at least \(\). We show that every graph of size \(\) has a bipartition in which the Edwards bound holds, and in addition each vertex class contains at most \(\) edges. This is exact for complete graphs of odd order, which we show are the only extremal graphs without isolated vertices. We also give results for partitions into more than two classes.

AMS Subject Classification (1991) Classes:  05C35 

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Copyright information

© János Bolyai Mathematical Society, 1999

Authors and Affiliations

  • B. Bollobás
    • 1
  • A. D. Scott
    • 2
  1. 1.Department of Pure Mathematics and Mathematical Statistics; 16 Mill Lane, Cambridge CB2 1SB, England and Department of Mathematical Sciences, University of Memphis; Memphis TN 38152; E-mail: bollobas@ibex.msci.memphis.eduUS
  2. 2.Department of Pure Mathematics and Mathematical Statistics; 16 Mill Lane, Cambridge CB2 1SB, England and Department of Mathematical Sciences, University of Memphis; Memphis, TN 38152 and Department of Mathematics, University College London; Gower Street, London WC1E 6BT; E-mail: scott@math.ucl.ac.ukUK

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