### Graphs which are both *H_1* and *H_2*-decomposable

Barbara Maenhaut
*Open University*

A graph *G* is said to be *H*-decomposable if there exists a collection of
subgraphs of *G*, each isomorphic to *H*, which partition the edge set of
*G*. If *G* is *H*-decomposable, we say that *H**|*G. Given two graphs
*H_1* and *H_2*, for which values *q* does there exist a graph *G*
having *q* edges such that *H_1|G* and *H_2|G*? The problem will
be considered for the cases when *H_1* and *H_2* are both cycles
and when *H_1* and *H_2* are both complete graphs.