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14,691
ON THE REALIZATION OF DOUBLE OCCURRENCE WORDS
, 709
"... Abstract. Let S be a double occurrence word, and let MS be the word’s interlacement matrix, regarded as a matrix over GF(2). Gauss addressed the question of which double occurrence words are realizable by generic closed curves in the plane. We reformulate answers given by Rosenstiehl and by de Frays ..."
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Fraysseix and Ossona de Mendez to give new graphtheoretic and algebraic characterizations of realizable words. Our algebraic characterization is especially pleasing: S is realizable if and only if there exists a diagonal matrix DS such that MS +DS is idempotent over GF(2). 1.
K5Free bound for the class of planar graphs
, 2006
"... We define kdiverse colouring of a graph to be a proper vertex colouring in which every vertex x sees min{k, d(x)} different colours in its neighbors. We show that for given k there is an f (k) for which every planar graph admits a kdiverse colouring using at most f (k) colours. Then using this col ..."
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this colouring we obtain a K 5free graph H for which every planar graph admits a homomorphism to it, and thus another proof for the result of J. Nesetril, P. Ossona de Mendez.
Domination Problems in NowhereDense Classes of Graphs
 LEIBNIZ INTERNATIONAL PROCEEDINGS IN INFORMATICS
"... We investigate the parameterized complexity of generalisations and variations of the dominating set problem on classes of graphs that are nowhere dense. In particular, we show that the distanced dominatingset problem, also known as the (k, d)centres problem, is fixedparameter tractable on any cl ..."
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Cited by 5 (4 self)
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that these graph classes are uniformly quasiwide, and does not rely on a structural decomposition. Our result also establishes that the distanced dominatingset problem is FPT on classes of bounded expansion, answering a question of Nesetril and Ossona de Mendez.
Abstract
, 907
"... We investigate the parameterized complexity of generalisations and variations of the dominating set problem on classes of graphs that are nowhere dense. In particular, we show that the distanced dominatingset problem, also known as the (k, d)centres problem, is fixedparameter tractable on any cla ..."
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that these graph classes are uniformly quasiwide, and does not rely on a structural decomposition. Our result also establishes that the distanced dominatingset problem is FPT on classes of bounded expansion, answering a question of Neˇsetˇril and Ossona de Mendez. 1
Characterisations of Nowhere Dense Graphs
, 2013
"... Nowhere dense classes of graphs were introduced by Nešetřil and Ossona de Mendez as a model for “sparsity” in graphs. It turns out that nowhere dense classes of graphs can be characterised in many different ways and have been shown to be equivalent to other concepts studied in areas such as (finite) ..."
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Nowhere dense classes of graphs were introduced by Nešetřil and Ossona de Mendez as a model for “sparsity” in graphs. It turns out that nowhere dense classes of graphs can be characterised in many different ways and have been shown to be equivalent to other concepts studied in areas such as (finite
Characterizations and Examples of Graph Classes with bounded expansion
"... Classes with bounded expansion, which generalise classes that exclude a topological minor, have recently been introduced by Neˇsetˇril and Ossona de Mendez. These classes are defined by the fact that the maximum average degree of a shallow minor of a graph in the class is bounded by a function of th ..."
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Cited by 2 (1 self)
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Classes with bounded expansion, which generalise classes that exclude a topological minor, have recently been introduced by Neˇsetˇril and Ossona de Mendez. These classes are defined by the fact that the maximum average degree of a shallow minor of a graph in the class is bounded by a function
Neˇsetˇril: NP by means of lifts and shadows
 MFCS’07, Lecture
"... Abstract. We show that every NP problem is polynomially equivalent to a simple combinatorial problem: the membership problem for a special class of digraphs. These classes are defined by means of shadows (projections) and by finitely many forbidden colored (lifted) subgraphs. Our characterization is ..."
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Cited by 6 (0 self)
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richness of coloring problems when restricted to most frequent graph classes. Using results of Neˇsetˇril and Ossona de Mendez for bounded expansion classes (which include bounded degree and proper minor closed classes) we prove that the restriction of every class defined as the shadow of finitely many
UNIVERSAL STRUCTURES AND THE LOGIC OF FORBIDDEN PATTERNS
, 2009
"... We show that forbidden patterns problems, when restricted to some classes of input structures, are in fact constraint satisfaction problems. This contrasts with the case of unrestricted input structures, for which it is known that there are forbidden patterns problems that are not constraint satisf ..."
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and generalises that of Neˇsetˇril and Ossona de Mendez’s, who investigated restricted dualities, which corresponds in our setting to investigating the restricted case when the considered forbidden patterns problems are captured by a firstorder sentence. Note also that our result holds in the general setting
Query Evaluation with Constant Delay
"... I am grateful to Luc Segoufin who kindly accepted me to be his PhD student. He introduced me to the problem of query enumeration and encouraged me to look for the answers to all the questions that emerged during our collaboration. He was a truly great advisor, always supportive and available for dis ..."
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for discussions and advice. I would like to thank Arnaud Durand and Patrice Ossona de Mendez for accepting to review this thesis and for their constructive comments on the earlier versions of this manuscript. Many thanks to Nicole Bidoit and Victor Vianu for accepting to be in my jury. Special thanks go to my
Deciding firstorder properties for sparse graphs
"... We present a lineartime algorithm for deciding firstorder logic (FOL) properties in classes of graphs with bounded expansion. Many natural classes of graphs have bounded expansion: graphs of bounded treewidth, all proper minorclosed classes of graphs, graphs of bounded degree, graphs with no sub ..."
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Cited by 29 (1 self)
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existential properties or the existence of short paths between prescribed vertices in such classes of graphs. All our results also hold for relational structures and are based on the seminal result of Nesetril and Ossona de Mendez on the existence of low treedepth colorings.
Results 1  10
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14,691