Version 5.0 The LEDA User Manual

12.12 Euler Tours ( euler tour )
An Euler tour in an undirected graph G is a cycle using every edge of G exactly once. A
graph has an Euler tour if it is connected and the degree of every vertex is even.
bool Euler Tour(const graph& G, list& T )
The function returns true if the undirected version of
G has an Euler tour. The Euler tour is returned in
T . The items in T are of the form (e, ± + 1), where
the second component indicates the traversal direction
d of the edge. If d = +1, the edge is traversed in
forward direction, and if d = −1, the edge is traversed
in reverse direction. The running time is O(n + m).
bool Check Euler Tour(const graph& G, const list& T )
bool Euler Tour(graph& G, list& T )
returns true if T is an Euler tour in G. The running
time is O(n + m).
The function returns true if the undirected verion of
G has an Euler tour. G is reoriented such that every
node has indegree equal to its outdegree and an Euler
tour (of the reoriented graph) is returned in T . The
running time is O(n + m).
bool Check Euler Tour(const graph& G, const list& T )
returns true if T is an Euler tour in the directed graph
G. The running time is O(n + m).