Vincent Limouzy

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We investigate the class of vertex intersection graphs of paths on a grid, and specifically consider the subclasses that are obtained when each path in the representation has at most k bends (turns). We call such a subclass the Bk-VPG graphs, k ≥ 0. In chip manufacturing, circuit layout is modeled as paths (wires) on a grid, where it is natural to constrain(More)
A dominating set D in a graph is a subset of its vertex set such that each vertex is either in D or has a neighbour in D. In this paper, we are interested in an output-sensitive enumeration algorithm of (inclusionwise) minimal dominating sets in graphs, called Dom problem. It was known that this problem can be polynomially reduced to the well known(More)
We prove that line graphs and path graphs have bounded neighbourhood Helly. As a consequence, we obtain output-polynomial time algorithms for enumerating the set of minimal dominating sets of line graphs and path graphs. Therefore, there exists an output-polynomial time algorithm that enumerates the set of minimal edge-dominating sets of any graph.
We investigate the class of vertex intersection graphs of paths on a grid, and specifically consider the subclasses that are obtained when each path in the representation has at most k bends (turns). We call such a subclass the Bk-VPG graphs, k ≥ 0. If the number k of bends is not restricted, then the VPG graphs are shown to be equivalent to the well-known(More)
A hypergraph is a pair pV, Eq where V is a finite set and E Ď 2 is called the set of hyper-edges. An output-polynomial algorithm for C Ď 2 is an algorithm that lists without repetitions all the elements of C in time polynomial in the sum of the size of H and the accumulated size of all the elements in C. Whether there exists an output-polynomial algorithm(More)
A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs, the terminology " module " not only captures the classical graph modules but also allows to handle 2−connected(More)
In this paper, a new general decomposition theory inspired from modular graph decomposition is presented. Our main result shows that, within this general theory, most of the nice algorithmic tools developed for modular decomposition are still efficient. This theory not only unifies the usual modular decomposition generalisations such as modular(More)