# Ticket #8786: trac_8786-other_fixes.2.patch

File trac_8786-other_fixes.2.patch, 7.4 KB (added by mvngu, 11 years ago)
• ## sage/graphs/digraph.py

```# HG changeset patch
# User Nathann Cohen <nathann.cohen@gmail.com>
# Date 1272441720 -7200
# Node ID 5af3155634cd101e69191b123948f78e6981b931
# Parent  4a624097a97bdd20e5bcc484ae37bc9425adbb57
#8786: added fixes: autogenerated broken links to Wikipedia

diff --git a/sage/graphs/digraph.py b/sage/graphs/digraph.py```
 a Directed graph. A digraph or directed graph is a set of vertices connected by oriented edges (cf. http://en.wikipedia.org/wiki/Digraph_%28mathematics%29 ). edges. `Wikipedia article on digraphs `_ One can very easily create a directed graph in Sage by typing:: Equivalently, a minimum feedback arc set of a DiGraph is a set `S` of arcs such that the digraph `G-S` is acyclic. For more informations, see ( http://en.wikipedia.org/wiki/Feedback_arc_set ) `Wikipedia article on Feedback arc sets `_. INPUT : Equivalently, a minimum feedback vertex set of a DiGraph is a set `S` of vertices such that the digraph `G-S` is acyclic. For more informations, see ( http://en.wikipedia.org/wiki/Feedback_vertex_set ) `Wikipedia article on Feedback vertex sets `_. INPUT :
• ## sage/graphs/digraph_generators.py

`diff --git a/sage/graphs/digraph_generators.py b/sage/graphs/digraph_generators.py`
 a In this digraph, there is an arc `w_1w_2` if `w_2` can be obtained from `w_1` by removing the leftmost letter and adding a new letter at its right end. ( more information on this page : http://en.wikipedia.org/wiki/De_Bruijn_graph ) `Wikipedia article on the De Bruijn graph `_ INPUT:
• ## sage/graphs/generic_graph.py

`diff --git a/sage/graphs/generic_graph.py b/sage/graphs/generic_graph.py`
 a A minimum edge cut between two vertices `s` and `t` of self is a set `A` of edges of minimum weight such that the graph obtained by removing `A` from self is disconnected. ( cf. http://en.wikipedia.org/wiki/Cut_%28graph_theory%29 ) `Wikipedia article on cuts `_. INPUT: A vertex cut between two non adjacent vertices is a set `U` of vertices of self such that the graph obtained by removing `U` from self is disconnected. ( cf. http://en.wikipedia.org/wiki/Cut_%28graph_theory%29 ) `Wikipedia article on cuts `_ INPUT: vertices such that each edge is incident to at least one element of `S`, and such that `S` is of minimum cardinality. ( cf. http://en.wikipedia.org/wiki/Vertex_cover ) `Wikipedia article on vertex cover `_. Equivalently, a vertex cover is defined as the complement of an independent set. Equivalently, a minimum feedback arc set of a DiGraph is a set `S` of arcs such that the digraph `G-S` is acyclic. For more informations, see ( http://en.wikipedia.org/wiki/Feedback_arc_set ) `Wikipedia article on feedback arc sets `_. INPUT : Equivalently, a minimum feedback vertex set of a DiGraph is a set `S` of vertices such that the digraph `G-S` is acyclic. For more informations, see ( http://en.wikipedia.org/wiki/Feedback_vertex_set ) `Wikipedia article on Feedback vertex sets `_. INPUT : def max_cut(self,value_only=True,use_edge_labels=True, vertices=False): r""" Returns a maximum edge cut of the graph ( cf. http://en.wikipedia.org/wiki/Cut_%28graph_theory%29 ) `Wikipedia article on cuts `_. INPUT: def flow(self,x,y,value_only=True,integer=False, use_edge_labels=True,vertex_bound=False): r""" Returns a maximum flow in the graph from ``x`` to ``y`` ( cf. http://en.wikipedia.org/wiki/Max_flow_problem ) represented by an optimal valuation of the edges. `Wikipedia article on flows `_. As an optimization problem, is can be expressed this way : .. MATH:: def matching(self,value_only=False, use_edge_labels=True): r""" Returns a maximum weighted matching of the graph ( cf. http://en.wikipedia.org/wiki/Matching ) represented by the list of its edges. `Wikipedia article on matchings `_. Given a graph `G` such that each edge `e` has a weight `w_e`, a maximum matching is a subset `S` of the edges of `G` of maximum weight such that no two edges of `S` are incident def dominating_set(self, independent=False, value_only=False,log=0): r""" Returns a minimum dominating set of the graph ( cf. http://en.wikipedia.org/wiki/Dominating_set ) represented by the list of its vertices. `Wikipedia article on dominating sets `_. A minimum dominating set `S` of a graph `G` is a set of its vertices of minimal cardinality such that any vertex of `G` is in `S` or has one of its neighbors def edge_connectivity(self,value_only=True,use_edge_labels=False, vertices=False): r""" Returns the edge connectivity of the graph ( cf. http://en.wikipedia.org/wiki/Connectivity_(graph_theory) ) `Wikipedia article on connectivity `_. INPUT: def vertex_connectivity(self,value_only=True, sets=False): r""" Returns the vertex connectivity of the graph ( cf. http://en.wikipedia.org/wiki/Connectivity_(graph_theory) ) `Wikipedia article on connectivity `_. INPUT: A Lex BFS ( or Lexicographic Breadth-First Search ) is a Breadth First Search used for the recognition of Chordal Graphs. More information on this page : http://en.wikipedia.org/wiki/Lexicographic_breadth-first_search `Wikipedia article on Lex-BFS `_ INPUT: