Contractible edges and contractible triangles in a 3-connected graph
For a 3-connected graph \(G\), an edge (resp. a triangle) of \(G\) is a 3-contractible edge (resp. a 3-contractible triangle) if the graph obtained from \(G\) by contracting it is also a 3-connected graph. Let \(E_c(G), \mathcal{T}_c(G)\) be the set of 3-contractible edges of \(G\) and the set of 3-contractible triangles of \(G\), respectively. In this paper, the authors prove that if \(G\) is a 3-connected graph of order at least 7, then \(|E_c(G)|+\frac{15}{14}|\mathcal{T}_c(G)|\geq \frac{6}{7}|V(G)|\). They also construct the extremal graphs to show the sharpness of their result.
scientific article; zbMATH DE number 7433381