Geodesic
Distribution of Contractible Edges and the Structure of Noncontractible Edges having Endvertices with Large Degree in a 4-Connected Graph
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 4, pp. 1051-1066.

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Let G be a 4-connected graph G, and let Ec(G) denote the set of 4-contractible 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-1(e)| ≤ 4 for each e ∈ Ec(G).
Keywords: 4-connected graph, contractible edge, cross free 
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Nakamura, Shunsuke. Distribution of Contractible Edges and the Structure of Noncontractible Edges having Endvertices with Large Degree in a 4-Connected Graph. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 4, pp. 1051-1066. http://geodesic.mathdoc.fr/item/DMGT_2021_41_4_a11/

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