Abstract
An edge of a 3-connected graph is calledcontractible if its contraction results in a 3-connected graph. Ando, Enomoto and Saito proved that every 3-connected graph of order at least five has ⌈|G|/2⌉ or more contractible edges. As another lower bound, we prove that every 3-connected graph, except for six graphs, has at least (2|E(G)| + 12)/7 contractible edges. We also determine the extremal graphs. Almost all of these extremal graphsG have more than ⌈|G|/2⌉ contractible edges.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ando, K., Enomoto, H., Saito, A.: Contractible edges in 3-connected graphs. J. Comb. Theory (B)42, 87–93 (1987)
Ando, K.: (private communication.)
Behzad, M., Chartrand G., Lesniak-Foster, L.: Graphs & Digraphs, Prindle, Weber & Schmidt, Boston, MA: 1979
Tutte, W.T.: A theory of 3-connected graphs, Indagationes Math.23, 441–455 (1961)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ota, K. The number of contractible edges in 3-connected graphs. Graphs and Combinatorics 4, 333–354 (1988). https://doi.org/10.1007/BF01864172
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01864172