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Circuit Double Cover of Graphs by Cun-Quan Zhang

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13Orientable cover

Attempts to prove the CDC conjecture have led to various conjectured strengthenings, such as the faithful circuit cover problem (Problem 2.1.4), strong circuit double cover problem (Conjecture 1.5.1), even covering problems (Conjectures 2.4.1 and 2.4.2), 5-even subgraph double cover problem (Conjecture 4.1.4), etc. Verification of any of those stronger problems will imply the CDC conjecture.

In this chapter, we present another type of variation of the double cover problem: directed circuit double covering. These are, in general, much stronger than the CDC problem. And some of them have already been completely characterized.

Historically, the paper by Tutte [229] on orientable circuit double cover is the earliest published article ...

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