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

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

Let G = ( V , E ) be a graph. A k -neighborhood in G is a set of vertices consisting of all the vertices at distance at most k from some vertex of G . The hypergraph on vertex set V whose edge set… Expand

— The problem of estimating the probability p = P (g(X) ≤ 0) is considered when X represents a multivariate stochastic input of a monotonic function g. First, a heuristic method to bound p,… 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