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Multicut is FPT
TLDR
We show that there exists an O(k)nc algorithm which decides if there exists a multicut of size at most k. Expand
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The Erdős-Hajnal conjecture for paths and antipaths
TLDR
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
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Recoloring bounded treewidth graphs
TLDR
A graph is k-mixing if any proper k-coloring can be transformed into any other through a sequence of adjacent properk-colorings. Expand
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A Polynomial Kernel for Multicut in Trees
TLDR
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
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Recoloring graphs via tree decompositions
TLDR
We prove that any graph is $(tw+2)$-mixing, where $tw$ is the treewidth of the graph (Cereceda 2006). Expand
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VC-dimension and Erdős-Pósa property
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 setExpand
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Clique versus independent set
TLDR
We show that three classical problems from communication complexity, graph theory and CSP are polynomially equivalent. Expand
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The Erdös-Hajnal Conjecture for Long Holes and Antiholes
TLDR
We prove that graphs which contain neither a hole of length at least k nor its complement have the Erdős-Hajnal property. Expand
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Accelerated Monte Carlo estimation of exceedance probabilities under monotonicity constraints
— 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
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Fast Recoloring of Sparse Graphs
TLDR
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
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