@article{f5af19f181b64e4eaf9f3281681f16ea, title = "Removable edges in a cycle of a 4-connected graph", abstract = "Let G be a 4-connected graph. For an edge e of G, we do the following operations on G: first, delete the edge e from G, resulting in the graph G - e; second, for all the vertices x of degree 3 in G - e, delete x from G - e and then completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we use single edges to replace them. The final resultant graph is denoted by G ⊖e. If G ⊖e is still 4-connected, then e is called a removable edge of G. In this paper, we investigate the problem on how many removable edges there are in a cycle of a 4-connected graph, and give examples to show that our results are in some sense the best possible. {\textcopyright} 2004 Elsevier B.V. All rights reserved.", keywords = "4-Connected graph, Edge-vertex-cut atom, Edge-vertex-cut fragment, Removable edge", author = "Jichang Wu and Xueliang Li and Lusheng Wang", year = "2004", month = oct, day = "28", doi = "10.1016/j.disc.2004.05.015", language = "English", volume = "287", pages = "103--111", journal = "Discrete Mathematics", issn = "0012-365X", publisher = "Elsevier BV * North-Holland", number = "1-3", }