On the size of identifying codes in triangle-free graphs
KLASING, Ralf
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
KOSOWSKI, Adrian
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Department of Algorithms and Systems Modelling [ETI GUT] [Gdansk University of Technology]
Voir plus >
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Department of Algorithms and Systems Modelling [ETI GUT] [Gdansk University of Technology]
KLASING, Ralf
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
KOSOWSKI, Adrian
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Department of Algorithms and Systems Modelling [ETI GUT] [Gdansk University of Technology]
< Réduire
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Department of Algorithms and Systems Modelling [ETI GUT] [Gdansk University of Technology]
Langue
en
Article de revue
Ce document a été publié dans
Discrete Applied Mathematics. 2012-07-01, vol. 160, n° 10-11, p. 1532-1546
Elsevier
Résumé en anglais
In an undirected graph $G$, a subset $C\subseteq V(G)$ such that $C$ is a dominating set of $G$, and each vertex in $V(G)$ is dominated by a distinct subset of vertices from $C$, is called an identifying code of $G$. The ...Lire la suite >
In an undirected graph $G$, a subset $C\subseteq V(G)$ such that $C$ is a dominating set of $G$, and each vertex in $V(G)$ 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, Chakrabarty and Levitin in 1998. For a given identifiable graph $G$, let $\M(G)$ be the minimum cardinality of an identifying code in $G$. In this paper, we show that for any connected identifiable triangle-free graph $G$ on $n$ vertices having maximum degree $\Delta\geq 3$, $\M(G)\le n-\tfrac{n}{\Delta+o(\Delta)}$. This bound is asymptotically tight up to constants due to various classes of graphs including $(\Delta-1)$-ary trees, which are known to have their minimum identifying code of size $n-\tfrac{n}{\Delta-1+o(1)}$. We also provide improved bounds for restricted subfamilies of triangle-free graphs, and conjecture that there exists some constant $c$ such that the bound $\M(G)\le n-\tfrac{n}{\Delta}+c$ holds for any nontrivial connected identifiable graph $G$.< Réduire
Mots clés en anglais
Identifying code
Dominating set
Triangle-free graph
Maximum degree
Project ANR
Approches dynamiques des Codes identifiants - ANR-08-EMER-0007
Origine
Importé de halUnités de recherche