Discriminating codes in bipartite graphs: bounds, extremal cardinalities, complexity

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November 2008, 2(4): 403-420. doi: 10.3934/amc.2008.2.403

Discriminating codes in bipartite graphs: bounds, extremal cardinalities, complexity

Emmanuel Charbit ^1, , Irène Charon ^2, , Gérard Cohen ^2, , Olivier Hudry ^2, and Antoine Lobstein ^2,

1.	Institut TELECOM, TELECOM ParisTech, 46, rue Barrault, 75634 Paris Cedex 13, France
2.	Institut TELECOM - TELECOM ParisTech, & Centre National de la Recherche Scientifique - LTCI UMR 5141, 46, rue Barrault, 75634 Paris Cedex 13, France, France, France, France

Received May 2008 Revised October 2008 Published November 2008

Abstract
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Consider an undirected bipartite graph $G=(V=I\cup A,E)$, with no edge inside $I$ nor $A$. For any vertex $v\in V$, let $N(v)$ be the set of neighbours of $v$. A code $C \subseteq A$ is said to be discriminating if all the sets $N(i) \cap C$, $i \in I$, are nonempty and distinct. We study some properties of discriminating codes. In particular, we give bounds on the minimum size of these codes, investigate graphs where minimal discriminating codes have size close to the upper bound, or give the exact minimum size in particular graphs; we also give an NP-completeness result.

Keywords: Graph theory, locating-dominating codes, bipartite graphs, discriminating codes, identifying codes, complexity, separating codes.

Mathematics Subject Classification: Primary: 05C99; Secondary: 94B65, 05C35, 68Q17.

Citation: Emmanuel Charbit, Irène Charon, Gérard Cohen, Olivier Hudry, Antoine Lobstein. Discriminating codes in bipartite graphs: bounds, extremal cardinalities, complexity. Advances in Mathematics of Communications, 2008, 2 (4) : 403-420. doi: 10.3934/amc.2008.2.403

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