# Ramsey equivalence of \$K_n\$ and \$K_n+K_{n-1}\$

@article{Bloom2018RamseyEO,
title={Ramsey equivalence of \\$K\_n\\$ and \\$K\_n+K\_\{n-1\}\\$},
author={Thomas F. Bloom and Anita Liebenau},
journal={The Electronic Journal of Combinatorics},
year={2018}
}
• Published 16 August 2015
• Mathematics
• The Electronic Journal of Combinatorics
We prove that, for \$n\geqslant 4\$, the graphs \$K_n\$ and \$K_n+K_{n-1}\$ are Ramsey equivalent. That is, if \$G\$ is such that any red-blue colouring of its edges creates a monochromatic \$K_n\$ then it must also possess a monochromatic \$K_n+K_{n-1}\$. This resolves a conjecture of Szabó, Zumstein, and Zürcher.The result is tight in two directions. Firstly, it is known that \$K_n\$ is not Ramsey equivalent to \$K_n+2K_{n-1}\$. Secondly, \$K_3\$ is not Ramsey equivalent to \$K_3+K_{2}\$. We prove that any graph…
3 Citations

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