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Judicious partitions of graphs

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 1993 United Kingdom English Publisher:Springer Science and Business Media LLCJournal:Periodica Mathematica Hungarica, volume 26, pages 125-137 (issn: 0031-5303, eissn: 1588-2829,

Authors: Bollobás, B; Scott, A;

doi: 10.1007/bf01876314

Judicious partitions of graphs

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Abstract

Let \(G\) be a graph and let \(e(G[V_ i])\) be the number of edges of the subgraph of \(G\) induced by \(V_ i\). Set \(p_ k(G) = \min (\max_{1 \leq i \leq k} e(G[V_ i]))\) where the minimum is taken over all partitions \(V_ 1, \dots, V_ k\) of the vertex set of \(G\) into \(k\) sets. It is proved that \(p_ k(G) \leq e(G) / {k+1 \choose 2}\). A better bound is given for graphs with many edges.

Country

United Kingdom

Related Organizations

University of Cambridge
United Kingdom
University of Oxford
United Kingdom

Keywords

Extremal problems in graph theory, partitions of graphs, bound, Extremal combinatorics, partitions

3 Research products, page of 1

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