# Martín Darío Safe

• Journal of Graph Theory
• 2008
A circular-arc graph is the intersection graph of a family of arcs on a circle. A characterization by forbidden induced subgraphs for this class of graphs is not known, and in this work we present a partial result in this direction. We characterize circular-arc graphs by a list of minimal forbidden induced subgraphs when the graph belongs to any of the(More)
• Discrete Applied Mathematics
• 2017
A normal Helly circular-arc graph is the intersection graph of arcs on a circle of which no three or less arcs cover the whole circle. Lin, Soulignac, and Szwarcfiter [Discrete Appl. Math. 2013] characterized circular-arc graphs that are not normal Helly circular-arc graphs, and used it to develop the first recognition algorithm for this graph class. As(More)
• Discrete Applied Mathematics
• 2009
A circle graph is the intersection graph of a family of chords on a circle. There is no known characterization of circle graphs by forbidden induced subgraphs that do not involve the notions of local equivalence or pivoting operations. We characterize circle graphs by a list of minimal forbidden induced subgraphs when the graph belongs to one of the(More)
A graph is concave-round if its vertices can be circularly enumerated so that the closed neighbourhood of each vertex is an interval in the enumeration. In this work, we give a minimal forbidden induced subgraph characterization for the class of concave-round graphs, solving a problem posed by Bang-Jensen, Huang, and Yeo [SIAM J Discrete Math, 13:179– 193,(More)
• Discrete Applied Mathematics
• 2013
The matching number of a graph is the maximum size of a set of vertexdisjoint edges. The transversal number is the minimum number of vertices needed to meet every edge. A graph has the König-Egerváry property if its matching number equals its transversal number. Lovász proved a characterization of graphs having the König-Egerváry property by means of(More)
• Discrete Mathematics & Theoretical Computer…
• 2014
CONICET and Depto. de Computación, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina CONICET and Depto. de Matemática and Instituto de Cálculo, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina, and Depto. de Ingenierı́a Industrial, FCFM, Universidad de Chile, Santiago, Chile Instituto de Ciencias, Universidad Nacional de General(More)
• Discrete Applied Mathematics
• 2016
Clique-width is a graph parameter with many algorithmic applications. For a positive integer k, the k-th power of a graph G is the graph with the same vertex set as G, in which two distinct vertices are adjacent if and only if they are at distance at most k in G. Many graph algorithmic problems can be expressed in terms of graph powers. We initiate the(More)
• ArXiv
• 2016
Given a simple graph G, a set C ⊆ V (G) is a neighborhood cover set if every edge and vertex of G belongs to some G[v] with v ∈ C, where G[v] denotes the subgraph of G induced by the closed neighborhood of the vertex v. Two elements of E(G)∪V (G) are neighborhood-independent if there is no vertex v ∈ V (G) such that both elements are in G[v]. A set S ⊆ V(More)