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 K4. If multiple edges occur, we use single edge to replace them. The final resultant graph is denoted by G e. If Ge 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. © 2008 KSCAM and Springer-Verlag.