Add to ORKGWe prove that, with high probability, in every 2-edge-colouring of the random tournament on n vertices there is a monochromatic copy of every oriented tree of order O(n/ \sqrt{log n}. This generalizes a result of the first, third and fourth authors, who proved the same statement for paths, and is tight up to a constant factor
Given an r-edge coloured complete graph Kn , how many monochromatic connected com- ponents does one ...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
AbstractRecently, Rödl and Ruciński [5,6] proved the following threshold result about Ramsey propert...
We prove that, with high probability, any 2‐edge‐coloring of a random tournament on n vertices conta...
An oriented graph is a directed graph with no bi-directed edges, i.e. if xy is an edge then yx is no...
We show that in every two-colouring of the edges of the complete graph K_N there is a monochromatic ...
In this thesis, we study several variations of the following fundamental problem in Ramsey theory: G...
We consider how large a tournament must be in order to guarantee the appearance of a given oriented ...
We prove that for every ℓ, r ≥ 3, there exists c > 0 such that for (image found), with high probabil...
AbstractWe call the tournament T an m-coloured tournament if the arcs of T are coloured with m colou...
Ramsey's Theorem guarantees for every graph H that any 2-edge-coloring of a sufficiently large compl...
AbstractLet T be a tournament and let c:e(T)→ {1,…,r} be an r-colouring of the edges of T. The assoc...
Extremal graph theory is concerned with the extreme values of a graph parameter over various classes...
<p>Starting from an innocent Ramsey-theoretic question regarding directed paths in tournaments, we d...
AbstractGiven a graph H, the size Ramsey number re(H,q) is the minimal number m for which there is a...
Given an r-edge coloured complete graph Kn , how many monochromatic connected com- ponents does one ...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
AbstractRecently, Rödl and Ruciński [5,6] proved the following threshold result about Ramsey propert...
We prove that, with high probability, any 2‐edge‐coloring of a random tournament on n vertices conta...
An oriented graph is a directed graph with no bi-directed edges, i.e. if xy is an edge then yx is no...
We show that in every two-colouring of the edges of the complete graph K_N there is a monochromatic ...
In this thesis, we study several variations of the following fundamental problem in Ramsey theory: G...
We consider how large a tournament must be in order to guarantee the appearance of a given oriented ...
We prove that for every ℓ, r ≥ 3, there exists c > 0 such that for (image found), with high probabil...
AbstractWe call the tournament T an m-coloured tournament if the arcs of T are coloured with m colou...
Ramsey's Theorem guarantees for every graph H that any 2-edge-coloring of a sufficiently large compl...
AbstractLet T be a tournament and let c:e(T)→ {1,…,r} be an r-colouring of the edges of T. The assoc...
Extremal graph theory is concerned with the extreme values of a graph parameter over various classes...
<p>Starting from an innocent Ramsey-theoretic question regarding directed paths in tournaments, we d...
AbstractGiven a graph H, the size Ramsey number re(H,q) is the minimal number m for which there is a...
Given an r-edge coloured complete graph Kn , how many monochromatic connected com- ponents does one ...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
AbstractRecently, Rödl and Ruciński [5,6] proved the following threshold result about Ramsey propert...