, Volume 4, Issue 1, pp 333-354

The number of contractible edges in 3-connected graphs

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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.