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The Bollobás-Thomason conjecture for 3-uniform hypergraphs

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Abstract

The vertices of any graph with m edges can be partitioned into two parts so that each part meets at least \(\frac{{2m}} {3}\) edges. Bollobás and Thomason conjectured that the vertices of any r-uniform graph may be likewise partitioned into r classes such that each part meets at least cm edges, with \(\frac{r} {{2r - 1}}\). In this paper, we prove this conjecture for the case r=3. In the course of the proof we shall also prove an extension of the graph case which was conjectured by Bollobás and Scott.

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Authors and Affiliations

  1. Trinity College, Cambridge, CB2 1TQ, UK

    John Haslegrave

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  1. John Haslegrave
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Correspondence to John Haslegrave.

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Research supported by the Engineering and Physical Sciences Research Council

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Haslegrave, J. The Bollobás-Thomason conjecture for 3-uniform hypergraphs. Combinatorica 32, 451–471 (2012). https://doi.org/10.1007/s00493-012-2696-x

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  • DOI: https://doi.org/10.1007/s00493-012-2696-x

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