  Given two graphs, a mapping between their edge-sets is cycle-continuous, if
the preimage of every cycle is a cycle. The motivation for this notion is
Jaeger's conjecture that for every bridgeless graph there is a cycle-continuous
mapping to the Petersen graph. Answering a question of DeVos, Ne\v{s}et\v{r}il,
and Raspaud, we prove that there exists an infinite set of graphs with no
cycle-continuous mapping between them. Further extending this result, we show
that every countable poset can be represented by graphs and existence of
cycle-continuous mappings between them.
