The Ramsey number R(G;H) has been actively studied for the past 40 years, and it was determined for a large family of pairs (G;H) of graphs. The Ramsey number of paths was determined very early on, but surprisingly very little is known about the Ramsey number for the powers of paths. The r-th power Pr n of a path on n vertices is obtained by joining any two vertices with distance at most r. We determine the exact value of R(P2 n; P2 n) for n large and discuss some related questions
The Ramsey number r(K 3,Q n ) is the smallest integer N such that every red-blue colouring of the ed...
Ramsey theory studies the existence of highly regular patterns in large sets of objects. Given two g...
In 1930, Frank Ramsey showed that one will find a monochromatic clique of a specified size in any ed...
The Ramsey number R(G;H) has been actively studied for the past 40 years, and it was determined for ...
AbstractThis note evaluates the Ramsey numbers r(Pm,Kn), and discusses developments in 0 generalized...
The Ramsey number $R(F,H)$ is the minimum number $N$ such that any $N$-vertex graph either contains ...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
This thesis contains new contributions to Ramsey theory, in particular results that establish exact ...
Given two graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N such that, for any ...
The Ramsey number r(Ks,Qn) is the smallest positive integer N such that every red–blue colouring of ...
Given a positive integer s, a graph G is s-Ramsey for a graph H, denoted G→(H)s, if every s-colourin...
A celebrated result of Chvátal, Rödl, Szemerédi and Trotter states (in slightly weakened form) that,...
The Ramsey number $R(r, b)$ is the least positive integer such that every edge 2-coloring of the com...
For any pair of graphs G and H, both the size Ramsey number ̂r(G,H) and the restricted size Ramsey n...
ABSTRACr. Let G be a connected graph on n vertices with no more than n(1 + e) edges, and Pk or Ck a ...
The Ramsey number r(K 3,Q n ) is the smallest integer N such that every red-blue colouring of the ed...
Ramsey theory studies the existence of highly regular patterns in large sets of objects. Given two g...
In 1930, Frank Ramsey showed that one will find a monochromatic clique of a specified size in any ed...
The Ramsey number R(G;H) has been actively studied for the past 40 years, and it was determined for ...
AbstractThis note evaluates the Ramsey numbers r(Pm,Kn), and discusses developments in 0 generalized...
The Ramsey number $R(F,H)$ is the minimum number $N$ such that any $N$-vertex graph either contains ...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
This thesis contains new contributions to Ramsey theory, in particular results that establish exact ...
Given two graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N such that, for any ...
The Ramsey number r(Ks,Qn) is the smallest positive integer N such that every red–blue colouring of ...
Given a positive integer s, a graph G is s-Ramsey for a graph H, denoted G→(H)s, if every s-colourin...
A celebrated result of Chvátal, Rödl, Szemerédi and Trotter states (in slightly weakened form) that,...
The Ramsey number $R(r, b)$ is the least positive integer such that every edge 2-coloring of the com...
For any pair of graphs G and H, both the size Ramsey number ̂r(G,H) and the restricted size Ramsey n...
ABSTRACr. Let G be a connected graph on n vertices with no more than n(1 + e) edges, and Pk or Ck a ...
The Ramsey number r(K 3,Q n ) is the smallest integer N such that every red-blue colouring of the ed...
Ramsey theory studies the existence of highly regular patterns in large sets of objects. Given two g...
In 1930, Frank Ramsey showed that one will find a monochromatic clique of a specified size in any ed...
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