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A grid graph is a node-induced finite subgraph of the infinite grid. It is rectangular if its set of nodes is the product of two intervals. Given a rectangular grid graph and two of its nodes, we give necessary and sufficient conditions for the graph to have a Hamilton path between these two nodes. In contrast, the Hamilton path (and circuit) problem for(More)
A graph G is said to be a bicluster graph if G is a disjoint union of bicliques (complete bipartite subgraphs), and a cluster graph if G is a disjoint union of cliques (complete subgraphs). In this work, we study the parameterized versions of the NP-hard Bicluster Graph Editing and Cluster Graph Editing problems. The former consists of obtaining a bicluster(More)
A circular-arc model ℳ is a circle C together with a collection $\mathcal{A}$ of arcs of C. If $\mathcal{A}$ satisfies the Helly Property then ℳ is a Helly circular-arc model. A (Helly) circular-arc graph is the intersection graph of a (Helly) circular-arc model. Circular-arc graphs and their subclasses have been the object of a great deal of attention in(More)
In this paper we present a modification of a technique by Chiba and Nishizeki [Chiba and Nishizeki: Arboricity and Subgraph Listing Algorithms, SIAM J. Comput. 14(1), pp. 210–223 (1985)]. Based on it, we design a data structure suitable for dynamic graph algorithms. We employ the data structure to formulate new algorithms for several problems , including(More)
Circular graphs are intersection graphs of arcs on a circle. These graphs are reported to have been studied since 1964, and they have been received considerable attention since a series of papers by Tucker in the 1970's. Various subclasses of circular-arc graphs have been also studied. Among these are the proper circular-arc graphs, unit circular-arc(More)
A stable matching is a complete matching of men and women such that no man and woman who are not partners both prefer each other to their actual partners under the matching. In an instance of the STABLE MARRIAGE problem, each of the n men and n women ranks the members of the opposite sex in order of preference. It is well known that at least one stable(More)