Exact Bounds for Judicious Partitions of Graphs

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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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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  • AMS Subject Classification (1991) Classes:  05C35