From 049c6ded29a4ce7f16d1a63c0ca90d7c782afacd Mon Sep 17 00:00:00 2001
From: Yu Cong <sxlxcsxlxc@gmail.com>
Date: Wed, 17 Dec 2025 13:55:12 +0800
Subject: [PATCH] fix bug

---
 main.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/main.tex b/main.tex
index 6ce3df9..fe4f092 100644
--- a/main.tex
+++ b/main.tex
@@ -163,7 +163,7 @@ Let $T$ be a spanning tree in the support of ideal tree packing.
 Recall that the number of inter-component edges of $T$ in $\mathcal P_F$ is $k$.
 Then we have
 \[
-\E_{F'}[|T\setminus F'|]=k\brack{1-\paren{\frac{k+1-k'}{k+1}}^2}\leq 2k'.
+\E_{F'}[|T\setminus F'|]\leq 2k \frac{k'}{k+1}\leq 2k'.
 \]
 \end{proof}