Path pile

Path pile --- путевая куча. A set of nontrivial paths in a graph [math]\displaystyle{ G }[/math] is called a path pile of [math]\displaystyle{ G }[/math], if every edge is on exactly one path and the paths are internally disjoint.

The least number which is the cardinality of a path pile of [math]\displaystyle{ G }[/math] is called the path pile number [math]\displaystyle{ \eta(G) }[/math] of [math]\displaystyle{ G }[/math].