Version 5.0 The LEDA User Manual

12.13 Algorithms for Planar Graphs (
plane graph alg )
node
bool
ST NUMBERING(const graph& G, node array& stnum,
list& stlist, edge e st = nil)
ST NUMBERING computes an st-numbering of G. If
e st is nil then t is set to some arbitrary node of G.
The node s is set to a neighbor of t and is returned.
If e st is not nil then s is set to the source of e st and
t is set to its target. The nodes of G are numbered
such that s has number 1, t has number n, and every
node v different from s and t has a smaller and a
larger numbered neighbor. The ordered list of nodes
is returned in stlist. If G has no nodes then nil is
returned and if G has exactly one node then this node
is returned and given number one.
Precondition: G is biconnected.
PLANAR(graph& , bool embed = false)
PLANAR takes as input a directed graph G(V, E) and
performs a planarity test for it. G must not contain
selfloops. If the second argument embed has value
true and G is a planar graph it is transformed into
a planar map (a combinatorial embedding such that
the edges in all adjacency lists are in clockwise ordering).
PLANAR returns true if G is planar and
false otherwise. The algorithm ([45]) has running time
O(|V | + |E|).
bool
PLANAR(graph& G, list& el, bool embed = false)
PLANAR takes as input a directed graph G(V, E) and
performs a planarity test for G. PLANAR returns
true if G is planar and false otherwise. If G is not
planar a Kuratowsky-Subgraph is computed and returned
in el.
bool
CHECK KURATOWSKI(const graph& G, const list& el)
returns true if all edges in el are edges of G and if the
edges in el form a Kuratowski subgraph of G, returns
false otherwise. Writes diagnostic output to cerr.