△-free→El≤n2/4 Second Proof. ∑(d+d)=d uw∈E u∈V △-free→du+d,≤n→∑(du+du)≤nlEl uv∈E Cauchy-Schwarz ( 2 4E2 (handshaking） m w∈V mE≥∑d+d)=∑≥②ev4)°- 4E2 m uv∈E v∈V m-free 㱺 |E| ≤ n2/4 Second Proof. ￾ uv￾E (du + dv) = ￾ v￾V d2 v u v (du + dv) Cauchy-Schwarz ⇤ v￾V d2 v ￾ 1 n ￾⇤ v￾V dv ⇥2 = 4|E| 2 n -free ⇥ du + dv ￾ n ⇥ ￾ uv￾E (du + dv) ￾ n|E| n|E| ￾ ⌅ uv￾E (du + dv) = ⌅ v￾V d2 v ￾ ￾⇤ v￾V dv ⇥2 n = 4|E| 2 n (handshaking)