AbstractThe Ramsey number r(H,Kn) is the smallest integer N so that each graph on N vertices that fails to contain H as a subgraph has independence number at least n. It is shown that r(K2,m,Kn)⩽(m−1+o(1))(n/logn)2 and r(C2m,Kn)⩽c(n/logn)m/(m−1) for m fixed and n→∞. Also r(K2,n,Kn)=Θ(n3/log2n) and r(C5,Kn)⩽cn3/2/logn
For fixed integers m,k≥2, it is shown that the k-color Ramsey number rk(Km,n) and the bipartite Rams...
The Ramsey number R(F, H) is the minimum number N such that any N-vertex graph either contains a cop...
AbstractUpper bounds are found for the Ramsey function. We prove R(3, x) < cx2lnx and, for each k ⩾ ...
We show that for any graph G with N vertices and average degree d, if the average degree of any neig...
The Ramsey numbers for a graph G versus a graph H, denoted by R(G,H) is the smallest positive intege...
The Ramsey numbers for a graph G versus a graph H, denoted by R(G,H) is the smallest positive intege...
AbstractP. Erdös, R.J. Faudree, C.C. Rousseau and R.H. Schelp [P. Erdös, R.J. Faudree, C.C. Rousseau...
AbstractIt is shown that a graph of orderNand average degreedthat does not contain the bookBm=K1+K1,...
AbstractRecently, the author (SIAM J. Discrete Math. 16 (2003) 99–113) has asymptotically computed (...
For a graph H and an integer n, theTurán number ex(n, H) isthemaximum possible number of edges in a ...
AbstractThe Ramsey number R(G1, G2) is the smallest integer p such that for any graph G on p vertice...
Given bipartite graphs H1 and H2, the bipartite Ramsey number b(H1;H2) is the smallest integer b suc...
AbstractIn this note we prove that the (diagonal) size Ramsey number of Kn.n is bounded below by 1/6...
Given bipartite graphs H1 and H2, the bipartite Ramsey number b(H1;H2) is the smallest integer b suc...
Let k ≥ 5 be a fixed integer and let m = ⌊(k - 1)/2⌋. It is shown that the independence number of a ...
For fixed integers m,k≥2, it is shown that the k-color Ramsey number rk(Km,n) and the bipartite Rams...
The Ramsey number R(F, H) is the minimum number N such that any N-vertex graph either contains a cop...
AbstractUpper bounds are found for the Ramsey function. We prove R(3, x) < cx2lnx and, for each k ⩾ ...
We show that for any graph G with N vertices and average degree d, if the average degree of any neig...
The Ramsey numbers for a graph G versus a graph H, denoted by R(G,H) is the smallest positive intege...
The Ramsey numbers for a graph G versus a graph H, denoted by R(G,H) is the smallest positive intege...
AbstractP. Erdös, R.J. Faudree, C.C. Rousseau and R.H. Schelp [P. Erdös, R.J. Faudree, C.C. Rousseau...
AbstractIt is shown that a graph of orderNand average degreedthat does not contain the bookBm=K1+K1,...
AbstractRecently, the author (SIAM J. Discrete Math. 16 (2003) 99–113) has asymptotically computed (...
For a graph H and an integer n, theTurán number ex(n, H) isthemaximum possible number of edges in a ...
AbstractThe Ramsey number R(G1, G2) is the smallest integer p such that for any graph G on p vertice...
Given bipartite graphs H1 and H2, the bipartite Ramsey number b(H1;H2) is the smallest integer b suc...
AbstractIn this note we prove that the (diagonal) size Ramsey number of Kn.n is bounded below by 1/6...
Given bipartite graphs H1 and H2, the bipartite Ramsey number b(H1;H2) is the smallest integer b suc...
Let k ≥ 5 be a fixed integer and let m = ⌊(k - 1)/2⌋. It is shown that the independence number of a ...
For fixed integers m,k≥2, it is shown that the k-color Ramsey number rk(Km,n) and the bipartite Rams...
The Ramsey number R(F, H) is the minimum number N such that any N-vertex graph either contains a cop...
AbstractUpper bounds are found for the Ramsey function. We prove R(3, x) < cx2lnx and, for each k ⩾ ...
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