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Circuit Double Cover of Graphs by Cun-Quan Zhang

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5Spanning minor, Kotzig frames

We continue the study of weight decomposition.

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 e ∈ E(G) (where wi(e) = 0 if e ∉ E(G)). (See Figure 3.1 where t = 2.)

In this chapter, we will further investigate how to find a set of three weighted graphs {(G1,w1), (G2,w2), (G3, w3)} for some families of cubic graphs G such that

(1) (G1, w1) + (G2, w2) + (G3, w3) is a weight decomposition of (G, 2),

(2) and each (Gj,wj) ...

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