203 citations · 470 across the 96 of their papers we have counts for
12 papers · 1 filter
Disjoint dijoins
Maria Chudnovsky, Katherine Edwards, Ringi Kim +2
A dijoin in a digraph is a set of edges meeting every directed cut. D. R. Woodall conjectured in 1976 that if G is a digraph, and every directed cut of G has at least k edges, then…
Disjoint paths in tournaments
Maria Chudnovsky, Paul Seymour, Alex Scott
Given pairs of vertices , , of a digraph , how can we test whether there exist vertex-disjoint directed paths from to for $1\le i\le…
Induced subgraphs of graphs with large chromatic number. II. Three steps towards Gyarfas' conjectures
Maria Chudnovsky, Paul Seymour, Alex Scott
Gyarfas conjectured in 1985 that for all , , every graph with no clique of size more than and no odd hole of length more than has chromatic number bounded by a functi…
Induced subgraphs of graphs with large chromatic number. I. Odd holes
Alex Scott, Paul Seymour
An odd hole in a graph is an induced subgraph which is a cycle of odd length at least five. In 1985, A. Gyarfas made the conjecture that for all t there exists n such that every gr…
Intersections of hypergraphs
Béla Bollobás, Alex Scott
Given two weighted k-uniform hypergraphs G, H of order n, how much (or little) can we make them overlap by placing them on the same vertex set? If we place them at random, how conc…
Packing random graphs and hypergraphs
Béla Bollobás, Svante Janson, Alex Scott
We determine to within a constant factor the threshold for the property that two random k-uniform hypergraphs with edge probability p have an edge-disjoint packing into the same ve…