Add to ORKGWe show that in every two-colouring of the edges of the complete graph K_N there is a monochromatic K_k which can be extended in at least (1 + o_(k)(1))2^(-k)N ways to a monochromatic K_(k+1). This result is asymptotically best possible, as may be seen by considering a random colouring. Equivalently, defining the book B_n^(k) to be the graph consisting of n copies of K_(k+1) all sharing a common K_k, we show that the Ramsey number r(B_n^(k)) = 2^(k)n + o_(k)(n). In this form, our result answers a question of Erdős, Faudree, Rousseau and Schelp and establishes an asymptotic version of a conjecture of Thomason
The Ramsey number r(G) of a graph G is the smallest number n such that, in any two-colouring of the ...
We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bou...
For s, t, n ∈ N with s ≥ t, an (s, t)-coloring of K$_n$ is an edge coloring of Kn in which each edge...
We show that in every two-colouring of the edges of the complete graph K_N there is a monochromatic ...
The book graph B^((k))_n consists of n copies of K_(k+1) joined along a common K_k. The Ramsey numbe...
The book graph B^((k))_n consists of n copies of K_(k+1) joined along a common K_k. The Ramsey numbe...
Ramsey’s theorem, in the version of Erdős and Szekeres, states that every 2-coloring of the edges of...
Ramsey’s theorem, in the version of Erdős and Szekeres, states that every 2-coloring of the edges of...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
Ramsey’s theorem, in the version of Erdős and Szekeres, states that every 2-coloring of the edges of...
Ramsey's theorem, in the version of Erdo{double acute}s and Szekeres, states that every 2-coloring o...
Ramsey's Theorem guarantees for every graph H that any 2-edge-coloring of a sufficiently large compl...
Extending an earlier conjecture of Erd\H{o}s, Burr and Rosta conjectured that among all two-coloring...
AbstractThe Ramsey number r(G) of a graph G is the minimum N such that every red–blue coloring of th...
The Ramsey number r(G) of a graph G is the smallest number n such that, in any two-colouring of the ...
We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bou...
For s, t, n ∈ N with s ≥ t, an (s, t)-coloring of K$_n$ is an edge coloring of Kn in which each edge...
We show that in every two-colouring of the edges of the complete graph K_N there is a monochromatic ...
The book graph B^((k))_n consists of n copies of K_(k+1) joined along a common K_k. The Ramsey numbe...
The book graph B^((k))_n consists of n copies of K_(k+1) joined along a common K_k. The Ramsey numbe...
Ramsey’s theorem, in the version of Erdős and Szekeres, states that every 2-coloring of the edges of...
Ramsey’s theorem, in the version of Erdős and Szekeres, states that every 2-coloring of the edges of...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
Ramsey’s theorem, in the version of Erdős and Szekeres, states that every 2-coloring of the edges of...
Ramsey's theorem, in the version of Erdo{double acute}s and Szekeres, states that every 2-coloring o...
Ramsey's Theorem guarantees for every graph H that any 2-edge-coloring of a sufficiently large compl...
Extending an earlier conjecture of Erd\H{o}s, Burr and Rosta conjectured that among all two-coloring...
AbstractThe Ramsey number r(G) of a graph G is the minimum N such that every red–blue coloring of th...
The Ramsey number r(G) of a graph G is the smallest number n such that, in any two-colouring of the ...
We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bou...
For s, t, n ∈ N with s ≥ t, an (s, t)-coloring of K$_n$ is an edge coloring of Kn in which each edge...