The Erdős-Sós conjecture for graphs whose complements contain no \(C_4\) (Q1884650)

Erdős and Sos conjectured in 1963 that every graph \(G\) with \(n\) vertices and \(e(G)\) edges contains every tree \(T\) with \(k\) edges, if \(e(G)> \frac 12 n(k-1)\). In this paper the authors prove the conjecture for graphs whose complements contain no cycles of length 4.