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The Unbalance of Set Systems

Authors:	Nathan Lemons Cory Palmer

Institution:	(1) Department of Mathematics and its Applications, Central European University, Nádor u. 9, Budapest, H-1051, Hungary

Abstract:	The unbalance of an intersecting family ${\mathcal{F}}F$ is defined as $\|{\mathcal{F}}\| - d({\mathcal{F}})$ , where $d({\mathcal{F}})$ is the maximum degree of ${\mathcal{F}}$ i.e. the maximum of $\|\{F \in {\mathcal{F}} : x \in F\}\|$ over all vertices x. We show that the unbalance of a k-uniform intersecting family is at most $\binom{n-3}{k-2}$ when n ≥ 6k ³ and we determine all families achieving this bound.

Keywords:	Intersecting set systems Intersecting families
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