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Circuit Double Cover of Graphs by Cun-Quan Zhang

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4Small oddness

4.1 k-even subgraph double covers

Recall Definition 3.1.1 for weight decomposition. Let (G, w) be an eulerian weighted graph. A set of eulerian weighted subgraphs {(Gi, wi) : i = 1, …, t} is called an eulerian weight decomposition of (G, w) if each Gi is a subgraph of G and images for every eE(G) (where wi(e) = 0 if eE(Gi)). (See Figure 3.1 where t = 2.)

Weight decomposition is an approach to the circuit double cover conjecture: if one can find a weight decomposition images of (G, 2) such that each (Gi, wi) has a faithful circuit cover (where ...

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