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Jaeger's directed cycle double cover conjecture can be formulated as aproblem of existence of special perfect matchings in a class of graphs that wecall hexagon graphs. In this work, we explore the structure of hexagon graphs.We show that hexagon graphs are braces that can be generated from the ladder on8 vertices using two types of McCuaig's augmentations.

Directed cycle double covers: structure and generation of hexagon graphs