Let G be a 4-connected graph. We call an edge e of G removable if the following sequence of operations results in a 4-connected graph: Delete e from G; if there are vertices with degree 3 in G-e, then for each (of the at most two) such vertex x, delete x from G-e and turn the three neighbors of x into a clique by adding any missing edges (avoiding multiple edges). In this paper, we continue the study on the distribution of removable edges in a 4-connected graph G, in particular outside a cycle of G or in a spanning tree or on a Hamilton cycle of G. We give examples to show that our results are in some sense best possible.
- 4-Connected graph
- Removable edge