Network


Latest external collaboration on country level. Dive into details by clicking on the dots.

Hotspot


Dive into the research topics where Florent Foucaud is active.

Publication


Featured researches published by Florent Foucaud.


European Journal of Combinatorics | 2011

Extremal graphs for the identifying code problem

Florent Foucaud; Eleonora Guerrini; Matjaz Kovse; Reza Naserasr; Aline Parreau; Petru Valicov

An identifying code of a graph G is a dominating set C such that every vertex x of G is distinguished from other vertices by the set of vertices in C that are at distance at most 1 from x. The problem of finding an identifying code of minimum possible size turned out to be a challenging problem. It was proved by N. Bertrand, I. Charon, O. Hudry and A. Lobstein that if a graph on n vertices with at least one edge admits an identifying code, then a minimal identifying code has size at most n-1. They introduced classes of graphs whose smallest identifying code is of size n-1. Few conjectures were formulated to classify the class of all graphs whose minimum identifying code is of size n-1. In this paper, disproving these conjectures, we classify all finite graphs for which all but one of the vertices are needed to form an identifying code. We classify all infinite graphs needing the whole set of vertices in any identifying code. New upper bounds in terms of the number of vertices and the maximum degree of a graph are also provided.


Journal of Graph Theory | 2013

IDENTIFYING CODES IN LINE GRAPHS

Florent Foucaud; Sylvain Gravier; Reza Naserasr; Aline Parreau; Petru Valicov

An identifying code of a graph is a subset of its vertices such that every vertex of the graph is uniquely identified by the set of its neighbours within the code. We study the edge-identifying code problem, i.e. the identifying code problem in line graphs. If


workshop on graph theoretic concepts in computer science | 2015

Algorithms and Complexity for Metric Dimension and Location-domination on Interval and Permutation Graphs

Florent Foucaud; George B. Mertzios; Reza Naserasr; Aline Parreau; Petru Valicov

\ID(G)


Discrete Applied Mathematics | 2016

Locating-dominating sets in twin-free graphs

Florent Foucaud; Michael A. Henning; Christian Löwenstein; Thomas Sasse

denotes the size of a minimum identifying code of an identifiable graph


SIAM Journal on Discrete Mathematics | 2015

LARGE SUBGRAPHS WITHOUT SHORT CYCLES

Florent Foucaud; Michael Krivelevich; Guillem Perarnau

G


Journal of Discrete Algorithms | 2015

Decision and approximation complexity for identifying codes and locating-dominating sets in restricted graph classes

Florent Foucaud

, we show that the usual bound


Discrete Mathematics | 2017

The complexity of signed graph and edge-coloured graph homomorphisms

Richard C. Brewster; Florent Foucaud; Pavol Hell; Reza Naserasr

\ID(G)\ge \lceil\log_2(n+1)\rceil


Theoretical Computer Science | 2017

Identification, location–domination and metric dimension on interval and permutation graphs. I. Bounds

Florent Foucaud; George B. Mertzios; Reza Naserasr; Aline Parreau; Petru Valicov

, where


Graphs and Combinatorics | 2013

Characterizing Extremal Digraphs for Identifying Codes and Extremal Cases of Bondy's Theorem on Induced Subsets

Florent Foucaud; Reza Naserasr; Aline Parreau

n


Discrete Applied Mathematics | 2017

The complexity of tropical graph homomorphisms

Florent Foucaud; Ararat Harutyunyan; Pavol Hell; Sylvain Legay; Yannis Manoussakis; Reza Naserasr

denotes the order of

Collaboration


Dive into the Florent Foucaud's collaboration.

Top Co-Authors

Avatar
Top Co-Authors

Avatar
Top Co-Authors

Avatar

Florian Sikora

Paris Dauphine University

View shared research outputs
Top Co-Authors

Avatar
Top Co-Authors

Avatar

Guillem Perarnau

Polytechnic University of Catalonia

View shared research outputs
Top Co-Authors

Avatar
Top Co-Authors

Avatar
Top Co-Authors

Avatar
Top Co-Authors

Avatar

Cristina Bazgan

Paris Dauphine University

View shared research outputs
Top Co-Authors

Avatar

Eun Jung Kim

Paris Dauphine University

View shared research outputs
Researchain Logo
Decentralizing Knowledge