Ramsey equivalence of Kn and Kn + Kn−1 - Bloom, TF; Liebenau, A (Electronic Journal of Combinatorics, 2018)
We prove that, for n ≥ 4, the graphs Kn and Kn + Kn−1 are Ramsey equivalent. That is, if G is such that any red-blue colouring of its edges creates a monochromatic Kn then it must also possess a monochromatic Kn + Kn−1. This resolves a conjecture of Szabó, Zumstein, and Zürcher [10].