Removable edges of cycles in 5-connected graphs

Let G be a 5-connected graph. For an edge e of G, we do the following operations on G: first, delete the edge e from G, resulting the graph G?e; second, for each vertex x of degree 4 in G?e, delete x from G?e and then completely connect the 4 neighbors of x by K ₄. If multiple edges occur, we use single edge to replace them. The final resultant graph is denoted by G ? e. If G ? e is still 5-connected, then e is called a removable edge of G. In this paper, we investigate the distribution of removable edges in a cycle of a 5-connected graph. And we give examples to show some of our results are best possible in some sense.