Martín Darío Safe

On Stopping Criteria for Genetic Algorithms

In this work we present a critical analysis of various aspects associated with the specification of termination conditions for simple genetic algorithms. The study, which is based on the use of Markov chains, identifies the main difficulties that arise when one wishes to set meaningful upper bounds for the number of iterations required to guarantee the convergence of such algorithms with a given confidence level. The latest trends in the design of stopping rules for evolutionary algorithms in general are also put forward and some proposals to overcome existing limitations in this respect are suggested.

Graph classes with and without powers of bounded clique-width

We initiate the study of graph classes of power-bounded clique-width, that is, graph classes for which there exist integers k and ? such that the k th powers of the graphs are of clique-width at most ? . We give sufficient and necessary conditions for this property. As our main results, we characterize graph classes of power-bounded clique-width within classes defined by either one forbidden induced subgraph, or by two connected forbidden induced subgraphs. We also show that for every positive integer k , there exists a graph class such that the k th powers of graphs in the class form a class of bounded clique-width, while this is not the case for any smaller power.

Forbidden induced subgraphs of normal Helly circular-arc graphs: Characterization and detection

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 open problems, they ask for the forbidden induced subgraph characterization and a direct recognition algorithm for normal Helly circular-arc graphs, both of which are resolved by the current paper. Moreover, when the input is not a normal Helly circular-arc graph, our recognition algorithm finds in linear time a minimal forbidden induced subgraph as certificate.

Structural results on circular-arc graphs and circle graphs: A survey and the main open problems

Circular-arc graphs are the intersection graphs of open arcs on a circle. Circle graphs are the intersection graphs of chords on a circle. These graph classes have been the subject of much study for many years and numerous interesting results have been reported. Many subclasses of both circular-arc graphs and circle graphs have been defined and different characterizations formulated. In this survey, we summarize the most important structural results related to circular-arc graphs and circle graphs and present the main open problems.

Partial characterizations of circle graphs

An electrolytic membrane cell for the electrochemical production of an alkali metal hydrosulfite by the reduction of an alkali metal biosulfite component of a circulated aqueous catholyte solution is provided. The cell utilizes an improved extended surface multipass porous cathode, an improved catholyte flow path and a hydrophilically treated separator mesh that separates the cation exchange membrane from the anode.

On minimal forbidden subgraph characterizations of balanced graphs

Abstract A {0, 1}-matrix is balanced if it contains no square submatrix of odd order with exactly two 1s per row and per column. Balanced matrices lead to ideal formulations for both set packing and set covering problems. Balanced graphs are those graphs whose clique-vertex incidence matrix is balanced. While a forbidden induced subgraph characterization of balanced graphs is known, there is no such characterization by minimal forbidden induced subgraphs. In this work we provide minimal forbidden induced subgraph characterizations of balanced graphs restricted to some graph classes which also lead to polynomial time or even linear time recognition algorithms within the corresponding subclasses.

Clique-perfectness of complements of line graphs

Abstract The clique-transversal number τc(G) of a graph G is the minimum size of a set of vertices meeting all the cliques. The clique-independence number αc(G) of G is the maximum size of a collection of vertex-disjoint cliques. A graph is clique-perfect if these two numbers are equal for every induced subgraph of G. Unlike perfect graphs, the class of clique-perfect graphs is not closed under graph complementation nor is a characterization by forbidden induced subgraphs known. Nevertheless, partial results in this direction have been obtained. For instance, in [Bonomo, F., M. Chudnovsky and G. Duran, Partial characterizations of clique-perfect graphs I: Subclasses of claw-free graphs, Discrete Appl. Math. 156 (2008), pp. 1058–1082], a characterization of those line graphs that are clique-perfect is given in terms of minimal forbidden induced subgraphs. Our main result is a characterization of those complements of line graphs that are clique-perfect, also by means of minimal forbidden induced subgraphs. This implies an O(n2) time algorithm for deciding the clique-perfectness of complements of line graphs and, for those that are clique-perfect, finding αc and τc.

Balancedness of some subclasses of circular-arc graphs☆

A graph is balanced if its clique-vertex incidence matrix contains no square submatrix of odd order with exactly two ones per row and per column. There is a characterization of balanced graphs by forbidden induced subgraphs, but no characterization by mininal forbidden induced subgraphs is known, not even for the case of circular-arc graphs. A circular-arc graph is the intersection graph of a family of arcs on a circle. In this work, we characterize when a given graph G is balanced in terms of minimal forbidden induced subgraphs, by restricting the analysis to the case where G belongs to certain classes of circular-arc graphs, including Helly circular-arc graphs, claw-free circular-arc graphs, and gem-free circular-arc graphs. In the case of gem-free circular-arc graphs, analogous characterizations are derived for two superclasses of balanced graphs: clique-perfect graphs and coordinated graphs.

Convex p-partitions of bipartite graphs

A set of vertices X of a graph G is convex if no shortest path between two vertices in X contains a vertex outside X. We prove that for fixed p ? 1 , all partitions of the vertex set of a bipartite graph into p convex sets can be found in polynomial time.

Forbidden subgraphs and the König-Egerváry property

The matching number of a graph is the maximum size of a set of vertex-disjoint edges. The transversal number is the minimum number of vertices needed to meet every edge. A graph has the Konig-Egervary property if its matching number equals its transversal number. Lovasz proved a characterization of graphs having the Konig-Egervary property by means of forbidden subgraphs within graphs with a perfect matching. Korach, Nguyen, and Peis proposed an extension of Lovaszs result to a characterization of all graphs having the Konig-Egervary property in terms of forbidden configurations (which are certain arrangements of a subgraph and a maximum matching). In this work, we prove a characterization of graphs having the Konig-Egervary property by means of forbidden subgraphs which is a strengthened version of the characterization by Korach et al. Using our characterization of graphs with the Konig-Egervary property, we also prove a forbidden subgraph characterization for the class of edge-perfect graphs.