The Number Of Removable Edges In 4-connected Graphs

Let G be a 4-connected graph and e E(G),Yin in [2]consider the following op-eration:(1) Delete e from G to get G-e,(2) If some endvertices of e have degree three in G-e, then supress them andmade their adjoint vertices each other,(3) If multiple edges occur after (2), then replace them by single edges tomake the graph simple.If the resulting graph is 3-connected, then e is said to be removable. If e is not removable, then e is said to be nonremovable.Yin in [2] proved that every 4-connected G of order at least six (exclude 2 cyclic graphe of order six)alwayse have removable edges.In this paper,we prove that every 4-connected graph of order at least six,except the 2 cyclic graph of order six , has at least (4;G|+16)/7 removableedges.We also characterize the graphs with (4|G +16)/7 removable edges.