Rémy Belmonte

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Boolean-width is a recently introduced graph width parameter. If a boolean decomposition of width w is given, several NP-complete problems, such as Maximum Weight Independent Set, k-Coloring and Minimum Weight Dominating Set are solvable in O∗(2O(w)) time [5]. In this paper we study graph classes for which we can compute a decomposition of logarithmic(More)
Modifying a given graph to obtain another graph is a wellstudied problem with applications in many fields. Given two input graphs G and H, the Contractibility problem is to decide whether H can be obtained from G by a sequence of edge contractions. This problem is known to be NP-complete already when both input graphs are trees of bounded diameter. We prove(More)
For a graph class G and any two positive integers i and j, the Ramsey number RG(i, j) is the smallest positive integer such that every graph in G on at least RG(i, j) vertices has a clique of size i or an independent set of size j. For the class of all graphs, Ramsey numbers are notoriously hard to determine, and they are known only for very small values of(More)
Motivated by recent results of Mathieson and Szeider (J. Comput. Syst. Sci. 78(1): 179–191, 2012), we study two graph modification problems where the goal is to obtain a graph whose vertices satisfy certain degree constraints. The Regular Contraction problem takes as input a graph G and two integers d and k, and the task is to decide whether G can be(More)
The k-DISJOINT PATHS problem, which takes as input a graph G and k pairs of specified vertices (si, ti), asks whether G contains k mutually vertexdisjoint paths Pi such that Pi connects si and ti, for i = 1, . . . , k. We study a natural variant of this problem, where the vertices of Pi must belong to a specified vertex subset Ui for i = 1, . . . , k. In(More)
The Contractibility problem takes as input two graphs G and H, and the task is to decide whether H can be obtained from G by a sequence of edge contractions. The Induced Minor and Induced Topological Minor problems are similar, but the first allows both edge contractions and vertex deletions, whereas the latter allows only vertex deletions and vertex(More)
For any graph class $$\mathcal{H}$$ H , the $$\mathcal{H}$$ H -Contraction problem takes as input a graph $$G$$ G and an integer $$k$$ k , and asks whether there exists a graph $$H\in \mathcal{H}$$ H ∈ H such that $$G$$ G can be modified into $$H$$ H using at most $$k$$ k edge contractions. We study the parameterized complexity of $$\mathcal{H}$$ H(More)
Given two graphs G and H, we say that G contains H as an induced minor if a graph isomorphic to H can be obtained from G by a sequence of vertex deletions and edge contractions. We study the complexity of Graph Isomorphism on graphs that exclude a fixed graph as an induced minor. More precisely, we determine for every graph H that Graph Isomorphism is(More)
We characterize all graphs that have carving-width at most k for k = 1, 2, 3. In particular, we show that a graph has carving-width at most 3 if and only if it has maximum degree at most 3 and treewidth at most 2. This enables us to identify the immersion obstruction set for graphs of carving-width at most 3.
For any graph class G and any two positive integers i and j, the Ramsey number RG(i, j) is the smallest positive integer such that every graph in G on at least RG(i, j) vertices has a clique of size i or an independent set of size j. For the class of all graphs, Ramsey numbers are notoriously hard to determine, and the exact values are known only for very(More)