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On the size of identifying codes in triangle-free graphs

hal.structure.identifierLaboratoire Bordelais de Recherche en Informatique [LaBRI]
dc.contributor.authorFOUCAUD, Florent
hal.structure.identifierLaboratoire Bordelais de Recherche en Informatique [LaBRI]
hal.structure.identifierAlgorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
dc.contributor.authorKLASING, Ralf
hal.structure.identifierLaboratoire Bordelais de Recherche en Informatique [LaBRI]
hal.structure.identifierAlgorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
hal.structure.identifierDepartment of Algorithms and Systems Modelling [ETI GUT] [Gdansk University of Technology]
dc.contributor.authorKOSOWSKI, Adrian
hal.structure.identifierLaboratoire Bordelais de Recherche en Informatique [LaBRI]
dc.contributor.authorRASPAUD, André
dc.date.accessioned2024-04-15T09:45:11Z
dc.date.available2024-04-15T09:45:11Z
dc.date.created2010-10-27
dc.date.issued2012-07-01
dc.identifier.issn0166-218X
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/197895
dc.description.abstractEnIn 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 $G$.
dc.description.sponsorshipApproches dynamiques des Codes identifiants - ANR-08-EMER-0007
dc.language.isoen
dc.publisherElsevier
dc.subject.enIdentifying code
dc.subject.enDominating set
dc.subject.enTriangle-free graph
dc.subject.enMaximum degree
dc.title.enOn the size of identifying codes in triangle-free graphs
dc.typeArticle de revue
dc.identifier.doi10.1016/j.dam.2012.02.009
dc.subject.halInformatique [cs]/Mathématique discrète [cs.DM]
dc.subject.halMathématiques [math]/Combinatoire [math.CO]
dc.identifier.arxiv1010.5975
bordeaux.journalDiscrete Applied Mathematics
bordeaux.page1532-1546
bordeaux.volume160
bordeaux.hal.laboratoriesLaboratoire Bordelais de Recherche en Informatique (LaBRI) - UMR 5800*
bordeaux.issue10-11
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00530172
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00530172v1
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