N. Bousquet

We show that there exists an O(k)nc algorithm which decides if there exists a multicut of size at most k. Expand

We prove that for every k, there exists c k 0 such that every graph G on n vertices with no induced path P k or its complement P k contains a clique or a stable set of size n c k . Expand

A graph is k-mixing if any proper k-coloring can be transformed into any other through a sequence of adjacent properk-colorings. Expand

The {\sc Multicut In Trees} problem consists in deciding, given a tree, a set of requests (i.e. paths in the tree) and an integer $k$, whether there exists aSet of $k$ edges cutting all the requests. Expand

We prove that any graph is $(tw+2)$-mixing, where $tw$ is the treewidth of the graph (Cereceda 2006). Expand

We show that three classical problems from communication complexity, graph theory and CSP are polynomially equivalent. Expand

We prove that graphs which contain neither a hole of length at least k nor its complement have the Erdős-Hajnal property. Expand

For every graph of maximum average degree bounded away from $d$, any $(d+1)$-coloring can be transformed into any other one within a polynomial number of vertex recolorings so that, at each step, the current coloring is proper. Expand