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A Disproof of the Fon-der-Flaass Conjecture

Published online by Cambridge University Press:  03 March 2004

J. ROBERT JOHNSON
J. ROBERT JOHNSON
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, UK (e-mail: J.R.Johnson@dpmms.cam.ac.uk)
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Abstract

Baranyai's partition theorem states that the edges of the complete $r$-graph on $n$ vertices can be partitioned into $1$-factors provided that $r$ divides $n$. Fon-der-Flaass has conjectured that for $r=3$ such a partitioning exists with the property that any two $1$-factors are ‘far apart’ in some natural sense.

Our aim in this note is to prove that the Fon-der-Flaass conjecture is not always true: it fails for $n=12$. Our methods are based on some new ‘auxiliary’ hypergraphs.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 13 , Issue 2 , March 2004 , pp. 195 - 201
Copyright
2004 Cambridge University Press

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