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Treewidth and Minimum Fill-in: Grouping the Minimal Separators
TLDR
We use the notion of potential maximal clique to characterize the maximal cliques appearing in minimal triangulations of a graph. Expand
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Listing all potential maximal cliques of a graph
TLDR
We show that the potential maximal cliques of a graph can be generated in polynomial time in the number of minimal separators of the graph. Expand
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Large Induced Subgraphs via Triangulations and CMSO
TLDR
We give an algorithm solving this optimization problem on any $n$-vertex graph $G$ in time ${\cal O}(|\Pi_G| \cdot n^{t+4}\cdot f(t,\varphi))$, where $\varphi$ is a counting monadic second order logic formula and $t\geq 0$ be an integer. Expand
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Exact (Exponential) Algorithms for Treewidth and Minimum Fill-In
TLDR
We show that for a graph G on n vertices its treewidth and minimum fill-in can be computed roughly in 1.9601 n time. Expand
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Distributed Testing of Excluded Subgraphs
TLDR
We show that, for every connected 4-node graph H, testing whether a graph is H-free can be done in a constant number of rounds, where the constant depends on how far the input graph is from being triangle-free. Expand
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Beyond Classes of Graphs with “Few” Minimal Separators: FPT Results Through Potential Maximal Cliques
TLDR
We introduce a generic optimization problem called Optimal Induced Subgraph for P and t , which encompasses those cited above and many others. Expand
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Exact Algorithms for Treewidth and Minimum Fill-In
TLDR
We show that the treewidth and the minimum fill-in of an $n$-vertex graph can be computed in time $\mathcal{O}(1.8899^n)$. Expand
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Chordal embeddings of planar graphs
TLDR
We give a new approach to tackle the problem of the treewidth computation for planar graphs which is much simpler than the proof of Lapoire. Expand
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Three Notes on Distributed Property Testing
TLDR
In this paper we present distributed property-testing algorithms for graph properties in the CONGEST model, with emphasis on testing subgraph-freeness. Expand
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Adding a Referee to an Interconnection Network: What Can(not) Be Computed in One Round
TLDR
In this paper we ask which properties of a distributed network can be computed from a few amount of local information provided by its nodes. Expand
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