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Exact Bounds for Judicious Partitions of Graphs

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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.

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Authors and Affiliations

  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.edu, , , , , , US

    B. Bollobás

  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.uk, , , , , , UK

    A. D. Scott

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  1. B. Bollobás
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  2. A. D. Scott
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Received: December 27, 1996/Revised: Revised June 10, 1998

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Bollobás, B., Scott, A. Exact Bounds for Judicious Partitions of Graphs. Combinatorica 19, 473–486 (1999). https://doi.org/10.1007/s004939970002

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  • DOI: https://doi.org/10.1007/s004939970002

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