AbstractLet D1,D2,…,Dk be acyclic digraphs. Define ρ(D1,D2,…,Dk) to be the minimum integer n such that every k-colouring of the transitive tournament TTn contains a monochromatic Di for some i. Let Cn,Sn and RTnh, respectively, denote the monotone cycle, the out-star and a rooted outgoing tree of height h on n vertices. Here, we find ρ(C3,Cn),ρ(RTn2,Sm) and ρ(D1,D2) for small acyclic digraphs D1 and D2
AbstractWe determine, to within a constant factor, the maximum size of a digraph that does not conta...
International audienceWe prove the existence of a function $h(k)$ such that every simple digraph wit...
AbstractFor an integer k≥1, the kth interleaved adjoint of a digraph G is the digraph ιk(G) with ver...
AbstractLet D1,D2,…,Dk be acyclic digraphs. Define ρ(D1,D2,…,Dk) to be the minimum integer n such th...
AbstractLet D1,D2,…,Dk be simple digraphs with no directed cycles. The ordered Ramsey number ρ(D1,D2...
AbstractThe Ramsey number r(D1,…,Dk) of acyclic directed graphs D1,…,Dk is defined as the largest in...
AbstractThe dichromatic number dk(D) of a digraph D is the minimum number of colours needed to colou...
AbstractGiven k directed graphs G1,…,Gk the Ramsey number R(G1,…, Gk) is the smallest integer n such...
AbstractWe prove that a tournament with n vertices has more than 0.13n2(1+o(1)) edge-disjoint transi...
We prove that, with high probability, any 2‐edge‐coloring of a random tournament on n vertices conta...
The study of problems concerning subdivisions of graphs has a rich history in extremal combinatorics...
We prove that, with high probability, in every 2-edge-colouring of the random tournament on n vertic...
AbstractFor an oriented graph G with n vertices, let f(G) denote the minimum number of transitive su...
AbstractLet T be a tournament and let c:e(T)→ {1,…,r} be an r-colouring of the edges of T. The assoc...
The oriented Ramsey number $\vec{r}(H)$ for an acyclic digraph $H$ is the minimum integer $n$ such t...
AbstractWe determine, to within a constant factor, the maximum size of a digraph that does not conta...
International audienceWe prove the existence of a function $h(k)$ such that every simple digraph wit...
AbstractFor an integer k≥1, the kth interleaved adjoint of a digraph G is the digraph ιk(G) with ver...
AbstractLet D1,D2,…,Dk be acyclic digraphs. Define ρ(D1,D2,…,Dk) to be the minimum integer n such th...
AbstractLet D1,D2,…,Dk be simple digraphs with no directed cycles. The ordered Ramsey number ρ(D1,D2...
AbstractThe Ramsey number r(D1,…,Dk) of acyclic directed graphs D1,…,Dk is defined as the largest in...
AbstractThe dichromatic number dk(D) of a digraph D is the minimum number of colours needed to colou...
AbstractGiven k directed graphs G1,…,Gk the Ramsey number R(G1,…, Gk) is the smallest integer n such...
AbstractWe prove that a tournament with n vertices has more than 0.13n2(1+o(1)) edge-disjoint transi...
We prove that, with high probability, any 2‐edge‐coloring of a random tournament on n vertices conta...
The study of problems concerning subdivisions of graphs has a rich history in extremal combinatorics...
We prove that, with high probability, in every 2-edge-colouring of the random tournament on n vertic...
AbstractFor an oriented graph G with n vertices, let f(G) denote the minimum number of transitive su...
AbstractLet T be a tournament and let c:e(T)→ {1,…,r} be an r-colouring of the edges of T. The assoc...
The oriented Ramsey number $\vec{r}(H)$ for an acyclic digraph $H$ is the minimum integer $n$ such t...
AbstractWe determine, to within a constant factor, the maximum size of a digraph that does not conta...
International audienceWe prove the existence of a function $h(k)$ such that every simple digraph wit...
AbstractFor an integer k≥1, the kth interleaved adjoint of a digraph G is the digraph ιk(G) with ver...
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