  An Eulerian-minor of an Eulerian graph is obtained from an Eulerian subgraph
of the Eulerian graph by contraction. The Eulerian-minor operation preserves
Eulerian properties of graphs and moreover Eulerian graphs are
well-quasi-ordered under Eulerian-minor relation. In this paper, we
characterize Eulerian, planar and outer-planar Eulerian graphs by means of
excluded Eulerian-minors, and provide a concise recursive characterization to
4-regular planar graphs.
