AbstractLet B, B1 and B2 be bipartite graphs, and let B→(B1,B2) signify that any red–blue edge-coloring of B contains either a red B1 or a blue B2. The size bipartite Ramsey number br̂(B1,B2) is defined as the minimum number of edges of a bipartite graph B such that B→(B1,B2). It is shown that br̂(Km,n,Km,n) is linear on n with m fixed, and br̂(Kn,n,Kn,n) is between c1n22n and c2n32n for some positive constants c1 and c2
For given graphs G1, . . . , Gk, the size-Ramsey number Rˆ(G1, . . . , Gk) is the smallest integer m...
AbstractWe calculate some size Ramsey numbers involving stars. For example we prove that for t ⩾ k ⩾...
AbstractFor given two graphs G1 and G2, and integer j ≥ 2, the size multipartite Ramsey numbers mj(G...
AbstractLet B, B1 and B2 be bipartite graphs, and let B→(B1,B2) signify that any red–blue edge-color...
AbstractIn this note we prove that the (diagonal) size Ramsey number of Kn.n is bounded below by 1/6...
The bipartite Ramsey number $BR(H_1,H_2,\ldots,H_k)$, is the smallest positive integer $b$, such tha...
The Ramsey number R(m, n) is the smallest integer p such that any blue-red colouring of the edges of...
AbstractLet H be a finite graph. The Ramsey size number of H, r̂(H,H), is the minimum number of edge...
AbstractFor bipartite graphs G1, G2, …, Gk, the bipartite Ramsey number b(G1, G2, …, Gk) is the leas...
Let $K_{l\times t}$ be a complete, balanced, multipartite graph consisting of $l$ partite sets and $...
AbstractFor fixed integers m,k⩾2, it is shown that the k-color Ramsey number rk(Km,n) and the bipart...
AbstractLet G and H be graphs. A graph with colored edges is said to be monochromatic if all its edg...
AbstractLet F, G, and H be finite, simple and undirected graphs. The connected size Ramsey number r̂...
AbstractThe Ramsey number R(G) of a graph G is the least integer p such that for all bicolorings of ...
AbstractRecently, the author (SIAM J. Discrete Math. 16 (2003) 99–113) has asymptotically computed (...
For given graphs G1, . . . , Gk, the size-Ramsey number Rˆ(G1, . . . , Gk) is the smallest integer m...
AbstractWe calculate some size Ramsey numbers involving stars. For example we prove that for t ⩾ k ⩾...
AbstractFor given two graphs G1 and G2, and integer j ≥ 2, the size multipartite Ramsey numbers mj(G...
AbstractLet B, B1 and B2 be bipartite graphs, and let B→(B1,B2) signify that any red–blue edge-color...
AbstractIn this note we prove that the (diagonal) size Ramsey number of Kn.n is bounded below by 1/6...
The bipartite Ramsey number $BR(H_1,H_2,\ldots,H_k)$, is the smallest positive integer $b$, such tha...
The Ramsey number R(m, n) is the smallest integer p such that any blue-red colouring of the edges of...
AbstractLet H be a finite graph. The Ramsey size number of H, r̂(H,H), is the minimum number of edge...
AbstractFor bipartite graphs G1, G2, …, Gk, the bipartite Ramsey number b(G1, G2, …, Gk) is the leas...
Let $K_{l\times t}$ be a complete, balanced, multipartite graph consisting of $l$ partite sets and $...
AbstractFor fixed integers m,k⩾2, it is shown that the k-color Ramsey number rk(Km,n) and the bipart...
AbstractLet G and H be graphs. A graph with colored edges is said to be monochromatic if all its edg...
AbstractLet F, G, and H be finite, simple and undirected graphs. The connected size Ramsey number r̂...
AbstractThe Ramsey number R(G) of a graph G is the least integer p such that for all bicolorings of ...
AbstractRecently, the author (SIAM J. Discrete Math. 16 (2003) 99–113) has asymptotically computed (...
For given graphs G1, . . . , Gk, the size-Ramsey number Rˆ(G1, . . . , Gk) is the smallest integer m...
AbstractWe calculate some size Ramsey numbers involving stars. For example we prove that for t ⩾ k ⩾...
AbstractFor given two graphs G1 and G2, and integer j ≥ 2, the size multipartite Ramsey numbers mj(G...
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