Clean up heavy vs. light vs. tree edges.

[saga.git] / mst.tex

diff --git a/mst.tex b/mst.tex
index 421fbc5adb52eaeda7011e70d30c79836f06f6e6..50e7bd23361459f730a08d1023cacd8e19008b17 100644 (file)
--- a/mst.tex
+++ b/mst.tex
@@ -75,12 +75,13 @@ Let~$T$ be a~spanning tree. Then:
   the edges of this path \df{edges covered by~$e$}.
 \:An edge~$e$ is called \df{light with respect to~$T$} (or just \df{$T$-light}) if it covers a heavier edge, i.e., if there
   is an edge $f\in T[e]$ such that $w(f) > w(e)$.
-\:An edge~$e$ is called \df{$T$-heavy} if it is not $T$-light.
+\:An edge~$e$ is called \df{$T$-heavy} if it covers a~lighter edge.
 \endlist
 
 \rem
-Please note that the above properties also apply to tree edges
-which by definition cover only themselves and therefore they are always heavy.
+Edges of the tree~$T$ itself are neither heavy nor light. We will sometimes
+use the name \df{non-heavy} for edges which are either light or contained
+in the tree.
 
 \lemman{Light edges}\id{lightlemma}%
 Let $T$ be a spanning tree. If there exists a $T$-light edge, then~$T$