## A tree edge \$uv\$ with \$u\$ as \$v\$’s parent is a cut edge if and only if there are no edges in \$v\$’s subtree that goes to \$u\$ or higher

A tree edge $$uv$$ with $$u$$ as $$v$$’s parent is a cut edge if and only if there are no edges in $$v$$’s subtree that goes to $$u$$ or higher.