diff --git a/.github/workflows/Downgrade.yml b/.github/workflows/Downgrade.yml
index d08d56609..ad93bdb6d 100644
--- a/.github/workflows/Downgrade.yml
+++ b/.github/workflows/Downgrade.yml
@@ -17,4 +17,6 @@ jobs:
     with:
       julia-version: "lts"
       group: "Core"
+      # Resolver.jl cannot minimum-resolve KrylovPreconditioners' historical Arpack/LightGraphs graph.
+      no_promote: "Mooncake,KrylovPreconditioners"
     secrets: "inherit"