TY - JOUR

T1 - The graph Ramsey number R(Fℓ,K6)

AU - Kadota, Shin ya

AU - Onozuka, Tomokazu

AU - Suzuki, Yuta

N1 - Funding Information:
The authors would like to thank Prof. Futaba Fujie for her comments and suggestions, which greatly improved the original manuscript. The authors also would like to thank the referees for their comments and remarks. The third author was supported by Grant-in-Aid for JSPS Research Fellow (Grant Number: JP16J00906 ).
Publisher Copyright:
© 2018 Elsevier B.V.

PY - 2019/4

Y1 - 2019/4

N2 - 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.

AB - 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.

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U2 - 10.1016/j.disc.2018.12.016

DO - 10.1016/j.disc.2018.12.016

M3 - Article

AN - SCOPUS:85059231409

VL - 342

SP - 1028

EP - 1037

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 4

ER -