Sentence:  Let "H" be a traversal of an undirected graph "G" = ("X", "U"). For given "H," the set "U" can be split into set of "tree edges" from the <WSD>forest</WSD> "G<sub>H</sub>" and the  set of "inverse" edges that do not belong to this <WSD>forest.</WSD> 
Meaning of the word marked with <WSD> tags:  A graph with no cycles; i.e., a graph made up of trees.