The Ramsey numbers of large cycles versus small wheels

Surahmat, E.T. Baskoro, H.J. Broersma

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Abstract

For two given graphs $G$ and $H$, the \textit{Ramsey number} $R(G,H)$ is the smallest positive integer $N$ such that for every graph $F$ of order $N$ the following holds: either $F$ contains $G$ as a subgraph or the complement of $F$ contains $H$ as a subgraph. In this paper, we determine the Ramsey number $R(C_n,W_{m})$ for $m=4$ and $m=5$. We show that $R(C_{n},W_{4})=2n-1$ and $R(C_n,W_5)=3n-2$ for $n\geq 5$. For larger wheels it remains an open problem to determine $R(C_n,W_{m})$.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages6
Publication statusPublished - 2002

Publication series

NameMemorandum
PublisherDepartment of Applied Mathematics, University of Twente
No.1634
ISSN (Print)0169-2690

Keywords

  • MSC-05C55
  • IR-65821
  • EWI-3454
  • MSC-05D10
  • METIS-208268

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