Ramsey degrees of bipartite graphs: A primitive recursive proof
نویسندگان
چکیده
منابع مشابه
Minimum Degrees of Minimal Ramsey Graphs
For graphs F and H, we say F is Ramsey for H if every 2-coloring of the edges of F contains a monochromatic copy of H. The graph F is Ramsey H-minimal if there is no proper subgraph F ′ of F so that F ′ is Ramsey for H. Burr, Erdős, and Lovász defined s(H) to be the minimum degree of F over all Ramsey H-minimal graphs F . Define Ht,d to be a graph on t+ 1 vertices consisting of a complete graph...
متن کاملAsymptotic Size Ramsey Results for Bipartite Graphs
We show that limn→∞ r̂(F1,n, . . . , Fq,n, Fp+1, . . . , Fr)/n exists, where the bipartite graphs Fq+1, . . . , Fr do not depend on n while, for 1 ≤ i ≤ q, Fi,n is obtained from some bipartite graph Fi with parts V1 ∪ V2 = V (Fi) by duplicating each vertex v ∈ V2 (cv + o(1))n times for some real cv > 0. In fact, the limit is the minimum of a certain mixed integer program. Using the Farkas Lemma ...
متن کاملRamsey Numbers of Some Bipartite Graphs Versus Complete Graphs
The Ramsey number r(H, Kn) is the smallest positive integer N such that every graph of order N contains either a copy of H or an independent set of size n. The Turán number ex(m, H) is the maximum number of edges in a graph of order m not containing a copy of H . We prove the following two results: (1) Let H be a graph obtained from a tree F of order t by adding a new vertex w and joining w to ...
متن کاملOn Bipartite Graphs with Linear Ramsey Numbers
We provide an elementary proof of the fact that the ramsey number of every bipartite graph H with maximum degree at most ∆ is less than 8(8∆)|V (H)|. This improves an old upper bound on the ramsey number of the n-cube due to Beck, and brings us closer toward the bound conjectured by Burr and Erdős. Applying the probabilistic method we also show that for all ∆≥1 and n≥∆+1 there exists a bipartit...
متن کاملSome Ramsey numbers for complete bipartite graphs
Upper bounds are determined for the Ramsey number ](m,n), 2 :; m n. These bounds are attained for infinitely many n in case of m 3 and are fairly close to the exact value for every m if n is sufficiently large.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2005
ISSN: 0012-365X
DOI: 10.1016/j.disc.2004.08.035