Abstract :
In this survey type article, various connections between eulerian graphs and other graph properties such as being hamiltonian, nowhere-zero flows, the cycle-plus-triangles problem and problems derived from it, are demonstrated. It is also shown how compatible cycle decompositions can be used to construct loopless 4-regular graphs having precisely one hamiltonian cycle, or to prove the equivalence between the Chinese Postman Problem and the Minimum Cycle Covering Problem in the planar bridgeless case.
