For a given pair of two graphs (F,H), let R(F,H) be the smallest positive integer r such that for any graph G of order r, either G contains F as a subgraph or the complement of G contains H as a subgraph. Baskoro, Broersma and Surahmat (2005) conjectured that R(Fℓ,Kn)=2ℓ(n−1)+1for ℓ≥n≥3, where Fℓ is the join K1+ℓK2 of K1 and ℓK2. In this paper, we prove that this conjecture is true for the case n=6.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics