Graph classes and Ramsey numbers
نویسندگان
چکیده
منابع مشابه
Graph classes and Ramsey numbers
For a graph class G and any two positive integers i and j, the Ramsey number RG(i, j) is the smallest positive integer such that every graph in G on at least RG(i, j) vertices has a clique of size i or an independent set of size j. For the class of all graphs, Ramsey numbers are notoriously hard to determine, and they are known only for very small values of i and j. Even if we restrict G to be ...
متن کاملOn Geometric Graph Ramsey Numbers
For any two-colouring of the segments determined by 3n− 3 points in general position in the plane, either the first colour class contains a triangle, or there is a noncrossing cycle of length n in the second colour class, and this result is tight. We also give a series of more general estimates on off-diagonal geometric graph Ramsey numbers in the same spirit. Finally we investigate the existen...
متن کاملMultipartite graph - space graph Ramsey numbers
The Ramsey number r(F, G) is the least number N such that in every two-coloring (R, B)=(red, blue) of the edges of KN , either there is a red copy of F or else a blue copy of G . The inequality (1) holds in view of the fact that the edges of the complete graph of order (m-1) (n-1) +s-1 can be given the coloring in which the blue graph, denoted (B), is isomorphic to (m-1)K„_~UKS_~ . Then the red...
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 کاملOn cycle - Complete graph ramsey numbers
A new upper bound is given for the cycle-complete graph Ramsey number r(C,,,, K„), the smallest order for a graph which forces it to contain either a cycle of order m or a set of ri independent vertices . Then, another cycle-complete graph Ramsey number is studied, namely r( :C,,,, K„) the smallest order for a graph which forces it to contain either a cycle of order 1 for some I satisfying 3 :1...
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 Applied Mathematics
سال: 2014
ISSN: 0166-218X
DOI: 10.1016/j.dam.2014.03.016