Now showing items 1-6 of 6

    • Centroidal bases in graphs 

      Foucaud, Florent; Klasing, Ralf; Slater, Peter J (2014-09-01)
      Article
      Open Access
      We introduce the notion of a centroidal locating set of a graph G, that is, a set L of vertices such that all vertices in G are uniquely determined by their relative distances to the vertices of L. A centroidal locating ...
    • Decision and approximation complexity for identifying codes and locating-dominating sets in restricted graph classes 

      Foucaud, Florent (2015-03-01)
      Article
      Open Access
      An identifying code is a subset of vertices of a graph with the property that each vertex is uniquely determined (identified) by its nonempty neighbourhood within the identifying code. When only vertices out of the code ...
    • Large subgraphs without short cycles 

      Foucaud, Florent; Krivelevich, Michael; Perarnau Llobet, Guillem (2015-01-06)
      Article
      Open Access
      We study two extremal problems about subgraphs excluding a family F of graphs. i) Among all graphs with m edges, what is the smallest size f(m, F) of a largest F–free subgraph? ii) Among all graphs with minimum degree d ...
    • Locating-dominating sets and identifying codes in Graphs of Girth at least 5 

      Balbuena Martínez, Maria Camino Teófila; Foucaud, Florent; Hansberg Pastor, Adriana (2015-04-29)
      Article
      Open Access
      Locating-dominating sets and identifying codes are two closely related notions in the area of separating systems. Roughly speaking, they consist in a dominating set of a graph such that every vertex is uniquely identified ...
    • Random subgraphs make identification affordable 

      Foucaud, Florent; Perarnau, Guillem; Serra Albó, Oriol (2017-01-02)
      Article
      Open Access
      An identifying code of a graph is a dominating set which uniquely determines all the vertices by their neighborhood within the code. Whereas graphs with large minimum degree have small domination number, this is not the ...
    • The complexity of homomorphisms of signed graphs and signed constraint satisfaction 

      Foucaud, Florent; Naserasr, Reza (2014)
      Conference report
      Open Access
      A signed graph (G,Σ) is an undirected graph G together with an assignment of signs (positive or negative) to all its edges, where Σ denotes the set of negative edges. Two signatures are said to be equivalent if one can be ...