On the size of identifying codes in triangle-free graphs - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2010

On the size of identifying codes in triangle-free graphs

Résumé

In an undirected graph $G=(V,E)$, a subset $C\subseteq V$ such that $C$ is a dominating set of $G$, and each vertex in $V$ is dominated by a distinct subset of vertices from $C$, is called an identifying code of $G$. The concept of identifying codes was introduced by Karpovsky et al. in 1998. Because of the variety of its applications, for example for fault-detection in networks or the location of fires in facilities, it has since been widely studied. For a given graph $G$, let $\M(G)$ be the minimum cardinality of an identifying code in $G$. In this paper, we show that for any connected triangle-free graph $G$ on $n$ vertices having maximum degree $\Delta\ge 2$, $\M(G)\le n-\frac{n}{3(\Delta+1)}$.
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Dates et versions

hal-00530172 , version 1 (27-10-2010)
hal-00530172 , version 2 (12-06-2011)
hal-00530172 , version 3 (29-06-2012)

Identifiants

Citer

Florent Foucaud, Ralf Klasing, Adrian Kosowski, André Raspaud. On the size of identifying codes in triangle-free graphs. 2010. ⟨hal-00530172v1⟩
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