Lower bounds on the Ramsey number r(G, H), as a function of the size ofthe graphs G and H, are determined. In particular, if H is a graph with n lines, lower bounds for r(H) = r(H,H) and r(Km, H) are calculated in terms of n in the first case and m and n in the second case. For m = 3 an upper bound is also determined. These results partially answer a question raised by Harary about the relationship between Ramsey numbers and the size of graphs.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics