New lower bounds for two multicolor classical Ramsey numbers
نویسندگان
چکیده
We present an algorithm to find lower bounds for multicolor classical Ramsey numbers by using 2-normalized cyclic graphs of prime order, and use it to obtain new lower bounds for two multicolor classical Ramsey numbers: R(3, 3, 12) ≥ 182, R(3, 3, 13) ≥ 212.
منابع مشابه
Constructive Lower Bounds on Classical Multicolor Ramsey Numbers
This paper studies lower bounds for classical multicolor Ramsey numbers, first by giving a short overview of past results, and then by presenting several general constructions establishing new lower bounds for many diagonal and off-diagonal multicolor Ramsey numbers. In particular, we improve several lower bounds for Rk(4) and Rk(5) for some small k, including 415 ≤ R3(5), 634 ≤ R4(4), 2721 ≤ R...
متن کاملNew lower bounds of fifteen classical Ramsey numbers
An algorithm to compute lower bounds for the classical Ramsey numbers R(Ql' Q2," " Qn) is developed. The decompositions of each of fifteen complete graphs of prime order into n circulant graphs are constructed and their properties are studied by computer search. This leads to new lower bounds of eight multicolor and seven 2-color Ramsey numbers, namely, R(3, 3, 6) 2: 54, R(3, 3, 7) 2: 72, R(3, ...
متن کاملA Note on Two Multicolor Ramsey Numbers
Two new bounds for multicolor Ramsey numbers are proved: R(K3,K3, C4, C4) ≥ 27 and R4(C4) ≤ 19.
متن کاملSymmetric Sum-Free Partitions and Lower Bounds for Schur Numbers
We give new lower bounds for the Schur numbers S(6) and S(7). This will imply new lower bounds for the Multicolor Ramsey Numbers R6(3) and R7(3). We also make several observations concerning symmetric sumfree partitions into 5 sets.
متن کاملZarankiewicz Numbers and Bipartite Ramsey Numbers
The Zarankiewicz number z(b; s) is the maximum size of a subgraph of Kb,b which does not contain Ks,s as a subgraph. The two-color bipartite Ramsey number b(s, t) is the smallest integer b such that any coloring of the edges of Kb,b with two colors contains a Ks,s in the rst color or a Kt,t in the second color.In this work, we design and exploit a computational method for bounding and computing...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006