Version 5.0 The LEDA User Manual

int KURATOWSKI(graph& G, list& V, list& E,
node array& deg)
KURATOWKI computes a Kuratowski subdivision K
of G as follows. V is the list of all nodes and subdivision
points of K. For all v ∈ V the degree deg[v] is
equal to 2 for subdivision points, 4 for all other nodes
if K is a K 5 , and -3 (+3) for the nodes of the left
(right) side if K is a K 3,3 . E is the list of all edges in
the Kuratowski subdivision.
list TRIANGULATE PLANAR MAP(graph& G)
TRIANGULATE PLANAR MAP takes a directed
graph G representing a planar map. It triangulates
the faces of G by inserting additional edges. The list
of inserted edges is returned.
Precondition: G must be connected.
The algorithm ([47]) has running time O(|V | + |E|).
void FIVE COLOR(graph& G, node array& C)
colors the nodes of G using 5 colors, more precisely,
computes for every node v a color C[v] ∈ {0, . . . , 4},
such that C[source(e)]! = C[target(e)] for every edge
e. Precondition: G is planar. Remark: works also
for many (sparse ?) non-planar graph.
void INDEPENDENT SET(const graph& G, list& I)
determines an independent set of nodes I in G. Every
node in I has degree at most 9. If G is planar and has
no parallel edges then I contains at least n/6 nodes.
bool Is CCW Ordered(const graph& G, const node array& x,
const node array& y)
checks whether the cyclic adjacency list of any node
v agrees with the counter-clockwise ordering of the
neighbors of v around v defined by their geometric
positions.
bool SORT EDGES(graph& G, const node array& x,
const node array& y)
reorders all adjacency lists such the cyclic adjacency
list of any node v agrees with the counter-clockwise
order of v’s neighbors around v defined by their geometric
positions. The function returns true if G is a
plane map after the call.