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- Hans L. Bodlaender, Stéphan Thomassé, Anders Yeo
- ESA
- 2009

In this paper, we give evidence for the problems Disjoint Cycles and Disjoint Paths that they cannot be preprocessed in polynomial time such that resulting instances always have a size bounded by a polynomial in a specified parameter (or, in short: do not have a polynomial kernel); these results are assuming the validity of certain complexity theoretic… (More)

- Stéphan Thomassé
- ACM Trans. Algorithms
- 2010

We prove that given an undirected graph <i>G</i> on <i>n</i> vertices and an integer <i>k</i>, one can compute, in polynomial time in <i>n</i>, a graph <i>G′</i> with at most 4<i>k</i><sup>2</sup> vertices and an integer <i>k′</i> such that <i>G</i> has a feedback vertex set of size at most <i>k</i> iff <i>G′</i> has a feedback vertex set… (More)

- Stéphane Bessy, Stéphan Thomassé
- J. Comb. Theory, Ser. B
- 2010

We prove that every graph G has a vertex partition into a cycle and an anticycle (a cycle in the complement of G). Emptyset, singletons and edges are considered as cycles. This problem was posed by Lehel and shown to be true for very large graphs by Luczak, Rödl and Szemerédi [7], and more recently for large graphs by Allen [1]. Many questions deal with the… (More)

- Stéphan Thomassé
- SODA
- 2009

We prove that given an undirected graph G on n vertices and an integer k, one can compute in polynomial time in n a graph G with at most 5k 2 +k vertices and an integer k such that G has a feedback vertex set of size at most k iff G has a feedback vertex set of size at most k. This result improves a previous O(k 11) kernel of Burrage et al. [6], and a more… (More)

- John Adrian Bondy, Jian Shen, Stéphan Thomassé, Carsten Thomassen
- Combinatorica
- 2006

We consider the problem of finding a large or dense triangle-free subgraph in a given graph G. In response to a question of P. Erd˝ os, we prove that, if the minimum degree of G is at least 17|V (G)|/20, the largest triangle-free subgraphs are precisely the largest bipartite subgraphs in G. We investigate in particular the case where G is a complete… (More)

- Frédéric Havet, Stéphan Thomassé
- Journal of Graph Theory
- 2000

We give a short constructive proof of a theorem of Fisher: every tournament contains a vertex whose second outneighborhood is as large as its ®rst outneighborhood. Moreover, we exhibit two such vertices provided that the tournament has no dominated vertex. The proof makes use of median orders. A second application of median orders is that every tournament… (More)

- Frédéric Havet, Stéphan Thomassé
- J. Comb. Theory, Ser. B
- 2000

- Nicolas Bousquet, Jean Daligault, Stéphan Thomassé
- STOC
- 2011

Let G=(V,E) be a graph on n vertices and R be a set of pairs of vertices in V called requests. A multicut is a subset F of E such that every request xy of R is cut by F, i.e. every xy-path of G intersects F. We show that there exists an O(f(k)n<sup>c</sup>) algorithm which decides if there exists a multicut of size at most k. In other words, the Multicut… (More)

- Stéphane Bessy, Fedor V. Fomin, +4 authors Stéphan Thomassé
- FSTTCS
- 2009

A tournament T = (V, A) is a directed graph in which there is exactly one arc between every pair of distinct vertices. Given a digraph on n vertices and an integer parameter k, the Feedback Arc Set problem asks whether the given digraph has a set of k arcs whose removal results in an acyclic digraph. The Feedback Arc Set problem restricted to tournaments is… (More)

- Omid Amini, Frédéric Mazoit, Nicolas Nisse, Stéphan Thomassé
- Discrete Mathematics
- 2009

Adapting the method introduced in Graph Minors X, we propose a new proof of the duality between the bramble-number of a graph and its tree-width. Our approach is based on a new definition of submodularity on partition functions which naturally extends the usual one on set functions. The proof does not rely on Menger's theorem, and thus greatly generalises… (More)