Luciano N. Grippo

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.

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.

On unit interval graphs with integer endpoints

Abstract We study those unit interval graphs having a model with intervals of prescribed integer length. We present a structural result for this subclass which leads to a quadratic–time recognition algorithm of it, giving as positive certificate a model of minimum total length and as negative certificate a forbidden induced subgraph.

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.

Forbidden subgraphs and the Kőnig property

Abstract A graph has the Kőnig property if its matching number equals its transversal number. Lovasz proved a characterization of graphs having the Kőnig property by forbidden subgraphs, restricted to graphs with a perfect matching. Korach, Nguyen, and Peis proposed an extension of Lovaszʼs result to a characterization of all graphs having the Kőnig property in terms of forbidden configurations (certain arrangements of a subgraph and a maximum matching). In this work, we prove a characterization of graphs having the Kőnig property in terms of forbidden subgraphs which is a strengthened version of the characterization by Korach et al. As a consequence of our characterization of graphs with the Kőnig property, we prove a forbidden subgraph characterization for the class of edge-perfect graphs.

Partial Characterizations of Circular-Arc Graphs

Abstract 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 the following classes: diamond-free graphs, P 4 -free graphs, paw-free graphs, and claw-free chordal graphs.

Domination parameters with number 2: interrelations and algorithmic consequences

In this paper, we study the most basic domination invariants in graphs, in which number 2 is intrinsic part of their definitions. We classify them upon three criteria, two of which give the following previously studied invariants: the weak