Jayme Luiz Szwarcfiter

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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 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)
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)
A Helly circular-arc modelM = (C,A) is a circle C together with a Helly family A of arcs of C. If no arc is contained in any other, thenM is a proper Helly circular-arc model, if every arc has the same length, then M is a unit Helly circular-arc model, and if there are no two arcs covering the circle, thenM is a normal Helly circular-arc model. A Helly(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 a recent paper, Durán, Gravano, McConnell, Spinrad and Tucker described an algorithm of complexity O(n2) for recognizing whether a graph G with n vertices and m edges is a unit circular-arc (UCA) graph. Furthermore the following open questions were posed in the above paper: (i) Is it possible to construct a UCA model for G in polynomial time?; (ii) Is it(More)