A graph G is covered by a set X of its subgraphs if each edge of G is contained in
at least one subgraph in X. The famous Four Colour Problem is equivalent to
covering a planar graph by two even subgraphs, which is also equivalent to the
existence of nowher-zero 4-flows in planar graphs. (An even graph is one that
can be covered by a set of edge-disjoint circuits.) This talk will focus on covering
a graph by circuits or paths.