Let G be a 3-connected graph. An edge (a triangle) of G is said to be a 3-contractible edge (a 3-contractible triangle) if the contraction of it results in a 3-connected graph. We denote by \(E_{c}(G)\) and \(\mathcal {T}_{c}(G)\) the set of 3-contractible edges of G and the set of 3-contractible triangles of G, respectively. We prove that if \(|V(G)|\ge 7\), then \(|E_{c}(G)|+ \frac{15}{14}|\mathcal {T}_{c}(G)|\ge \frac{6}{7}|V(G)|.\) We also determine the extremal graphs.

中文翻译：

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三连通图中的可收缩边和可收缩三角形

令G为三连通图。如果G 的边（三角形）的收缩导致 3-连通图，则称其为 3-可收缩边（3-可收缩三角形）。我们用\（E_ {C}（G）\）和\（\ mathcal【T} _ {C}（G）\）的组的3-收缩边的ģ和该组的3-收缩三角形ģ， 分别。我们证明如果\(|V(G)|\ge 7\)，那么\(|E_{c}(G)|+ \frac{15}{14}|\mathcal {T}_{c}( G)|\ge \frac{6}{7}|V(G)|.\)我们还确定了极值图。