Structure of edges in a 4-connected graph not contained in triangles and the number of contractible edges - Yoshimi Egawa (AKCE International Journal of Graphs and Combinatorics, 2018)
Let be a 4-connected graph, and let denote the set of those edges of which are not contained in a triangle, and let denote the set of 4-contractible edges of . We show that if or , then unless has one of the three specified configurations.