Combinatorica

, Volume 32, Issue 4, pp 451–471 | Cite as

The Bollobás-Thomason conjecture for 3-uniform hypergraphs

Original Paper

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.

Mathematics Subject Classification (2000)

05C35 05C65 

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Copyright information

© János Bolyai Mathematical Society and Springer Verlag 2012

Authors and Affiliations

  1. 1.Trinity CollegeCambridgeUK

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