Could someone give a precise definition of what 'edge disjoint union' means in graph theory? i.e. what does it mean to say a graph $G$ can be written as the edge disjoint union of graphs $H$, $K$?
I've been trying to look for a precise definition and annoyingly cannot find one.
Is it just a matter of $e(H)\sqcup e(K)=e(G)$? Or do we require the graph $H\cup K$ include all the vertices of $G$ as well (e.g. in the case that $G$ has isolated vertices with no edges which may not appear in $H,K$)