# HG changeset patch
# User Robert L. Miller
# Date 1276905940 25200
# Node ID bdaf0cf036ef5169bf326ec25abdcae06884fea4
# Parent 88286e3cf010031343a6759520fccacd12d10352
#8403 - fix #optional tags
diff -r 88286e3cf010 -r bdaf0cf036ef sage/graphs/generic_graph.py
--- a/sage/graphs/generic_graph.py Sun Feb 28 18:58:05 2010 +0100
+++ b/sage/graphs/generic_graph.py Fri Jun 18 17:05:40 2010 -0700
@@ -3096,8 +3096,8 @@
Definition :
Computing a minimum spanning tree in a graph can be done in `n
- \log(n)` time (and in linear time if all weights are
- equal). On the other hand, if one is given a large (possibly
+ \log(n)` time (and in linear time if all weights are equal) where
+ `n = V + E`. On the other hand, if one is given a large (possibly
weighted) graph and a subset of its vertices, it is NP-Hard to
find a tree of minimum weight connecting the given set of
vertices, which is then called a Steiner Tree.
@@ -3142,13 +3142,13 @@
of course, always a tree ::
sage: g = graphs.RandomGNP(30,.5)
- sage: st = g.steiner_tree(g.vertices()[:5]) # optional - requires GLPK, CBC or CPLEX
- sage: st.is_tree() # optional - requires GLPK, CBC or CPLEX
+ sage: st = g.steiner_tree(g.vertices()[:5]) # optional - GLPK, CBC
+ sage: st.is_tree() # optional - GLPK, CBC
True
And all the 5 vertices are contained in this tree ::
- sage: all([v in st for v in g.vertices()[:5] ]) # optional - requires GLPK, CBC or CPLEX
+ sage: all([v in st for v in g.vertices()[:5] ]) # optional - GLPK, CBC
True
An exception is raised when the problem is impossible, i.e.