Ramsey minimal graphs

Authors

Béla Bollobás, University of MemphisFollow
Jair Donadelli, Universidade de São Paulo
Yoshiharu Kohayakawa, Universidade de São Paulo
Richard H. Schelp, University of Memphis

Abstract

As usual, for graphs Γ, G, and H, we write Γ → (G, H) to mean that any red-blue colouring of the edges of Γ contains a red copy of G or a blue copy of H. A pair of graphs (G, H) is said to be Ramsey-infinite if there are infinitely many minimal graphs Γ for which we have Γ → (G, H). Let ℓ ≥ 4 be an integer. We show that if H is a 2-connected graph that does not contain induced cycles of length at least ℓ, then the pair (Ck, H) is Ramsey-infinite for any k ≥ ℓ, where Ck denotes the cycle of length k.

Publication Title

Journal of the Brazilian Computer Society

Recommended Citation

Bollobás, B., Donadelli, J., Kohayakawa, Y., & Schelp, R. (2001). Ramsey minimal graphs. Journal of the Brazilian Computer Society, 7 (3), 27-37. https://doi.org/10.1590/S0104-65002001000200005