Geodesic
Construction of codes identifying sets of vertices
The electronic journal of combinatorics, Tome 12 (2005)
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In this paper the problem of constructing graphs having a $(1,\le \ell)$-identifying code of small cardinality is addressed. It is known that the cardinality of such a code is bounded by $\Omega\left({\ell^2\over\log \ell}\log n\right)$. Here we construct graphs on $n$ vertices having a $(1,\le \ell)$-identifying code of cardinality $O\left(\ell^4 \log n\right)$ for all $\ell \ge 2$. We derive our construction from a connection between identifying codes and superimposed codes, which we describe in this paper.
DOI : 10.37236/1910
Classification : 05C99, 94B60, 94C12
Mots-clés : identifying codes 
@article{10_37236_1910,
     author = {Sylvain Gravier and Julien Moncel},
     title = {Construction of codes identifying sets of vertices},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1910},
     zbl = {1060.05091},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1910/}
}
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%A Julien Moncel
%T Construction of codes identifying sets of vertices
%J The electronic journal of combinatorics
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Sylvain Gravier; Julien Moncel. Construction of codes identifying sets of vertices. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1910

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