  We investigate the question how `small' a graph can be, if it contains all
members of a given class of locally finite graphs as subgraphs or induced
subgraphs. More precisely, we give necessary and sufficient conditions for the
existence of a connected, locally finite graph $H$ containing all elements of a
graph class $\mathcal G$. These conditions imply that such a graph $H$ exists
for the class $\mathcal G_d$ consisting of all graphs with maximum degree $<d$
which raises the question whether in this case $H$ can be chosen to have
bounded maximum degree. We show that this is not the case, thereby answering a
question recently posed by Huynh et al.
