Geodesic
Pairs of disjoint \(q\)-element subsets far from each other
The electronic journal of combinatorics, The Fraenkel Festschrift volume, Tome 8 (2001) no. 2
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Let $n$ and $q$ be given integers and $X$ a finite set with $n$ elements. The following theorem is proved for $n>n_0(q)$. The family of all $q$-element subsets of $X$ can be partitioned into disjoint pairs (except possibly one if $n\choose q$ is odd), so that $|A_1\cap A_2|+|B_1\cap B_2|\leq q$, $|A_1\cap B_2|+|B_1\cap A_2| \leq q$ holds for any two such pairs $\{ A_1,B_1\} $ and $\{ A_2,B_2\} $. This is a sharpening of a theorem in [2]. It is also shown that this is a coding type problem, and several problems of similar nature are posed.
DOI : 10.37236/1606
Classification : 05B30, 05C45, 94B99
Mots-clés : design, Hamiltonian cycle, code 
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     author = {Hikoe Enomoto and Gyula O. H. Katona},
     title = {Pairs of disjoint \(q\)-element subsets far from each other},
     journal = {The electronic journal of combinatorics},
     year = {2001},
     volume = {8},
     number = {2},
     doi = {10.37236/1606},
     zbl = {0981.05023},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1606/}
}
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Hikoe Enomoto; Gyula O. H. Katona. Pairs of disjoint \(q\)-element subsets far from each other. The electronic journal of combinatorics, The Fraenkel Festschrift volume, Tome 8 (2001) no. 2. doi: 10.37236/1606

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