Bollob\'as-Erdos-Tuza conjecture for graphs with no induced Kₒ, ₓ

A widely open conjecture proposed by Bollob\'as, Erdos, and Tuza in the early 1990s states that for any n-vertex graph G, if the independence number (G) = (n), then there is a subset T V (G) with |T| = o (n) such that T intersects all maximum independent sets of G. In this paper, we prove that this conjecture holds for graphs that do not contain an induced Kₒ, ₓ for fixed t s. Our proof leverages the probabilistic method at an appropriate juncture.