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Let G be a 4-connected graph G, and let Ec(G) denote the set of 4contractible edges of G. We prove results concerning the distribution of edges in Ec(G). Roughly speaking, we show that there exists a set K0 and a mapping φ : K0 → Ec(G) such that |φ (e)| ≤ 4 for each e ∈ Ec(G).

Distribution of contractible edges and the structure of noncontracible edges having endvertices with large degree in a 4-connected graph