From 6939e79c9b5f25af49b92732d6e54b67b7a40838 Mon Sep 17 00:00:00 2001 From: Martin Mares Date: Thu, 17 Jan 2008 00:33:36 +0100 Subject: [PATCH] A tiny remark. --- mst.tex | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/mst.tex b/mst.tex index d61cecb..51580d0 100644 --- a/mst.tex +++ b/mst.tex @@ -157,7 +157,8 @@ and thus $T$~is also minimal. In general, a single graph can have many minimal spanning trees (for example a complete graph on~$n$ vertices and unit edge weights has $n^{n-2}$ minimum spanning trees according to the Cayley's formula \cite{cayley:trees}). -However, this is possible only if the weight function is not injective. +However, as the following lemma shows, this is possible only if the weight +function is not injective. \lemman{MST uniqueness} If all edge weights are distinct, then the minimum spanning tree is unique. -- 2.39.2