1.1 --- a/lemon/graph_adaptor.h	Fri Feb 03 14:07:52 2006 +0000
     1.2 +++ b/lemon/graph_adaptor.h	Fri Feb 03 14:22:45 2006 +0000
     1.3 @@ -439,15 +439,15 @@
     1.4    /// SubGraphAdaptor shows the graph with filtered node-set and 
     1.5    /// edge-set. If the \c checked parameter is true then it filters the edgeset
     1.6    /// to do not get invalid edges without source or target.
     1.7 -  /// Let  \f$  G=(V, A)  \f$  be a directed graph
     1.8 +  /// Let \f$ G=(V, A) \f$ be a directed graph
     1.9    /// and suppose that the graph instance \c g of type ListGraph
    1.10 -  /// implements  \f$  G  \f$ .
    1.11 -  /// Let moreover  \f$  b_V  \f$  and  \f$  b_A  \f$  be bool-valued functions resp.
    1.12 +  /// implements \f$ G \f$.
    1.13 +  /// Let moreover \f$ b_V \f$ and \f$ b_A \f$ be bool-valued functions resp.
    1.14    /// on the node-set and edge-set.
    1.15    /// SubGraphAdaptor<...>::NodeIt iterates 
    1.16 -  /// on the node-set  \f$ \{v\in V : b_V(v)=true\} \f$  and 
    1.17 +  /// on the node-set \f$ \{v\in V : b_V(v)=true\} \f$ and 
    1.18    /// SubGraphAdaptor<...>::EdgeIt iterates 
    1.19 -  /// on the edge-set  \f$ \{e\in A : b_A(e)=true\} \f$ . Similarly, 
    1.20 +  /// on the edge-set \f$ \{e\in A : b_A(e)=true\} \f$. Similarly, 
    1.21    /// SubGraphAdaptor<...>::OutEdgeIt and
    1.22    /// SubGraphAdaptor<...>::InEdgeIt iterates 
    1.23    /// only on edges leaving and entering a specific node which have true value.
    1.24 @@ -1049,14 +1049,14 @@
    1.25    ///than the other
    1.26    ///parts of the lib. Use them at you own risk.
    1.27    ///
    1.28 -  /// Let  \f$  G=(V, A)  \f$  be a directed graph and for each directed edge 
    1.29 -  ///  \f$  e\in A  \f$ , let  \f$  \bar e  \f$  denote the edge obtained by
    1.30 +  /// Let \f$ G=(V, A) \f$ be a directed graph and for each directed edge 
    1.31 +  ///\f$ e\in A \f$, let \f$ \bar e \f$ denote the edge obtained by
    1.32    /// reversing its orientation. We are given moreover two bool valued 
    1.33    /// maps on the edge-set, 
    1.34 -  ///  \f$  forward\_filter  \f$ , and  \f$  backward\_filter  \f$ . 
    1.35 +  ///\f$ forward\_filter \f$, and \f$ backward\_filter \f$. 
    1.36    /// SubBidirGraphAdaptor implements the graph structure with node-set 
    1.37 -  ///  \f$  V  \f$  and edge-set 
    1.38 -  ///  \f$  \{e : e\in A \mbox{ and } forward\_filter(e) \mbox{ is true}\}+\{\bar e : e\in A \mbox{ and } backward\_filter(e) \mbox{ is true}\}  \f$ . 
    1.39 +  ///\f$ V \f$ and edge-set 
    1.40 +  ///\f$ \{e : e\in A \mbox{ and } forward\_filter(e) \mbox{ is true}\}+\{\bar e : e\in A \mbox{ and } backward\_filter(e) \mbox{ is true}\} \f$. 
    1.41    /// The purpose of writing + instead of union is because parallel 
    1.42    /// edges can arise. (Similarly, antiparallel edges also can arise).
    1.43    /// In other words, a subgraph of the bidirected graph obtained, which 
    1.44 @@ -1185,24 +1185,24 @@
    1.45    ///
    1.46    ///An adaptor for composing the residual graph for
    1.47    ///directed flow and circulation problems. 
    1.48 -  ///Let  \f$ G=(V, A) \f$  be a directed graph and let  \f$ F \f$  be a 
    1.49 +  ///Let \f$ G=(V, A) \f$ be a directed graph and let \f$ F \f$ be a 
    1.50    ///number type. Let moreover 
    1.51 -  /// \f$ f,c:A\to F \f$ , be functions on the edge-set. 
    1.52 -  ///In the appications of ResGraphAdaptor,  \f$ f \f$  usually stands for a flow 
    1.53 -  ///and  \f$ c \f$  for a capacity function.   
    1.54 +  ///\f$ f,c:A\to F \f$, be functions on the edge-set. 
    1.55 +  ///In the appications of ResGraphAdaptor, \f$ f \f$ usually stands for a flow 
    1.56 +  ///and \f$ c \f$ for a capacity function.   
    1.57    ///Suppose that a graph instange \c g of type 
    1.58 -  ///\c ListGraph implements  \f$ G \f$  .
    1.59 +  ///\c ListGraph implements \f$ G \f$.
    1.60    ///\code
    1.61    ///  ListGraph g;
    1.62    ///\endcode
    1.63    ///Then RevGraphAdaptor implements the graph structure with node-set 
    1.64 -  /// \f$ V \f$  and edge-set  \f$ A_{forward}\cup A_{backward} \f$ , where 
    1.65 -  /// \f$ A_{forward}=\{uv : uv\in A, f(uv)<c(uv)\} \f$  and 
    1.66 -  /// \f$ A_{backward}=\{vu : uv\in A, f(uv)>0\} \f$ , 
    1.67 +  ///\f$ V \f$ and edge-set \f$ A_{forward}\cup A_{backward} \f$, where 
    1.68 +  ///\f$ A_{forward}=\{uv : uv\in A, f(uv)<c(uv)\} \f$ and 
    1.69 +  ///\f$ A_{backward}=\{vu : uv\in A, f(uv)>0\} \f$, 
    1.70    ///i.e. the so called residual graph. 
    1.71 -  ///When we take the union  \f$ A_{forward}\cup A_{backward} \f$ , 
    1.72 +  ///When we take the union \f$ A_{forward}\cup A_{backward} \f$, 
    1.73    ///multilicities are counted, i.e. if an edge is in both 
    1.74 -  /// \f$ A_{forward} \f$  and  \f$ A_{backward} \f$ , then in the adaptor it 
    1.75 +  ///\f$ A_{forward} \f$ and \f$ A_{backward} \f$, then in the adaptor it 
    1.76    ///appears twice. 
    1.77    ///The following code shows how 
    1.78    ///such an instance can be constructed.