Order plus size of τ ‐critical graphs

Let G = ( V , E ) be a τ ‐critical graph with τ ( G ) = t . Erdős and Gallai proved that ∣ V ∣ ≤ 2 t and the bound ∣ E ∣ ≤t + 1 2was obtained by Erdős, Hajnal, and Moon. We give here the sharp combined bound ∣ E ∣ + ∣ V ∣ ≤t + 2 2and find all graphs with equality.