AbstractFor fixed integers m,k⩾2, it is shown that the k-color Ramsey number rk(Km,n) and the bipartite Ramsey number bk(m,n) are both asymptotically equal to kmn as n→∞, and that for any graph H on m vertices, the two-color Ramsey number r(H+K¯n,Kn) is at most (1+o(1))nm+1/(logn)m-1. Moreover, the order of magnitude of r(H+K¯n,Kn) is proved to be nm+1/(logn)m if H≠Km as n→∞
We study two problems in graph Ramsey theory. In the early 1970's, Erd\H{o}s and O'Neil considered a...
AbstractRecently, the author (SIAM J. Discrete Math. 16 (2003) 99–113) has asymptotically computed (...
AbstractP. Erdös, R.J. Faudree, C.C. Rousseau and R.H. Schelp [P. Erdös, R.J. Faudree, C.C. Rousseau...
AbstractFor fixed integers m,k⩾2, it is shown that the k-color Ramsey number rk(Km,n) and the bipart...
For fixed integers m,k≥2, it is shown that the k-color Ramsey number rk(Km,n) and the bipartite Rams...
AbstractLet B, B1 and B2 be bipartite graphs, and let B→(B1,B2) signify that any red–blue edge-color...
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...
AbstractIt is shown that the order of magnitude of Ramsey number R(K3,Kn,n) is n2/logn as n→∞
AbstractLet G and H be graphs. Results are given which, in principle, permit the Ramsey numbers r(G,...
AbstractThe Ramsey number R(G) of a graph G is the least integer p such that for all bicolorings of ...
AbstractGiven graphs G and H, a coloring of E(G) is called an (H,q)-coloring if the edges of every c...
AbstractUpper bounds are found for the Ramsey function. We prove R(3, x) < cx2lnx and, for each k ⩾ ...
For a graph $H$ and integer $k\ge1$, let $r(H;k)$ and $r_\ell(H;k)$ denote the $k$-color Ramsey numb...
AbstractIn this note we prove that the (diagonal) size Ramsey number of Kn.n is bounded below by 1/6...
We study two problems in graph Ramsey theory. In the early 1970's, Erd\H{o}s and O'Neil considered a...
AbstractRecently, the author (SIAM J. Discrete Math. 16 (2003) 99–113) has asymptotically computed (...
AbstractP. Erdös, R.J. Faudree, C.C. Rousseau and R.H. Schelp [P. Erdös, R.J. Faudree, C.C. Rousseau...
AbstractFor fixed integers m,k⩾2, it is shown that the k-color Ramsey number rk(Km,n) and the bipart...
For fixed integers m,k≥2, it is shown that the k-color Ramsey number rk(Km,n) and the bipartite Rams...
AbstractLet B, B1 and B2 be bipartite graphs, and let B→(B1,B2) signify that any red–blue edge-color...
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...
AbstractIt is shown that the order of magnitude of Ramsey number R(K3,Kn,n) is n2/logn as n→∞
AbstractLet G and H be graphs. Results are given which, in principle, permit the Ramsey numbers r(G,...
AbstractThe Ramsey number R(G) of a graph G is the least integer p such that for all bicolorings of ...
AbstractGiven graphs G and H, a coloring of E(G) is called an (H,q)-coloring if the edges of every c...
AbstractUpper bounds are found for the Ramsey function. We prove R(3, x) < cx2lnx and, for each k ⩾ ...
For a graph $H$ and integer $k\ge1$, let $r(H;k)$ and $r_\ell(H;k)$ denote the $k$-color Ramsey numb...
AbstractIn this note we prove that the (diagonal) size Ramsey number of Kn.n is bounded below by 1/6...
We study two problems in graph Ramsey theory. In the early 1970's, Erd\H{o}s and O'Neil considered a...
AbstractRecently, the author (SIAM J. Discrete Math. 16 (2003) 99–113) has asymptotically computed (...
AbstractP. Erdös, R.J. Faudree, C.C. Rousseau and R.H. Schelp [P. Erdös, R.J. Faudree, C.C. Rousseau...
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