Graphs and Combinatorics

, Volume 4, Issue 1, pp 333–354

The number of contractible edges in 3-connected graphs

  • Katsuhiro Ota

DOI: 10.1007/BF01864172

Cite this article as:
Ota, K. Graphs and Combinatorics (1988) 4: 333. doi:10.1007/BF01864172


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.

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Katsuhiro Ota
    • 1
  1. 1.Department of Information Science, Faculty of ScienceUniversity of TokyoTokyoJapan

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