`The immediately preceding paragraph identifies an Eulerian subgraph with the set of its edges, so symmetric difference would seem to apply here.  What I do not understand is the phrase: ``which is equivalent to only considering those even subgraphs which contain all vertices of the full graph.`` I cannot understand why this phrase (which seems to have been there since the beginning) is there, nothing seems to reply upon it (in fact it seems to be an error, since it would spoil the closure of the Eulerian subgraphs under symmetric difference if it were true).     `