Graphs and Combinatorics

, Volume 30, Issue 2, pp 267–274 | Cite as

Maximum Hitting for n Sufficiently Large

  • Ben Barber
Original Paper


For a left-compressed intersecting family \({\fancyscript{A} \subseteq[n]^{(r)}}\) and a set \({X \subseteq [n]}\) , let \({\fancyscript{A}(X) = \{A \in \fancyscript{A} : A \cap X \neq \emptyset\}}\) . Borg asked: for which X is \({|\fancyscript{A}(X)|}\) maximised by taking \({\fancyscript{A}}\) to be all r-sets containing the element 1? We determine exactly which X have this property, for n sufficiently large depending on r.


Intersecting family Compression Generating set Erdős–Ko–Rado theorem 


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Copyright information

© Springer Japan 2013

Authors and Affiliations

  1. 1.Department of Pure Mathematics and Mathematical StatisticsCentre for Mathematical SciencesCambridgeUK

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