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Discussiones Mathematicae Graph Theory 32(2) (2012)
379-382
DOI: https://doi.org/10.7151/dmgt.1620
Erdös--Ko--Rado from Intersecting Shadows
| Gyula O.H. Katona and Ákos Kisvölcsey
Alfréd Rényi Institute of Mathematics, |
Abstract
A set system is called t-intersecting if every two members meet each other in at least t elements. Katona determined the minimum ratio of the shadow and the size of such families and showed that the Erdős-Ko-Rado theorem immediately follows from this result. The aim of this note is to reproduce the proof to obtain a slight improvement in the Kneser graph. We also give a brief overview of corresponding results.
Keywords: Kneser graph, coclique, intersecting family, shadow
2010 Mathematics Subject Classification: 05C35, 05D05.
References
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Received 28 April 2011
Revised 6 August 2011
Accepted 8 August 2011
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