**Hint for Exercise 1.1.** See Section 1.4 and Conjecture 1.4.4.

**Hint for Exercise 1.2.** It is possible that the circuit decomposition of 2*G* may contain a digon, which corresponds to a single edge of the original graph *G* (not a circuit).

**Hint for Exercise 1.3.** The union of * and the symmetric difference of all members of * forms an even subgraph double cover of the graph. (See Definition A.2.3 for the definition ...

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