Contractible edges in 3-connected graphs
An edge whose contraction results in a 3-connected graph is called a contractible edge. Using two theorems of \textit{R. Halin} [Math. Ann. 182, 175-188 (1969; Zbl 0175.505); Abh. Sem. Univ. Hamburg 33, 133-163 (1969; Zbl 0175.505)] it is easy to see that every 3-connected graph G of order least five has \(\lceil (| G| +3)/5\rceil\) or more contractible edges. The authors improved this bound to \(\lceil | G| /2\rceil\) and characterizes those 3-connected graphs which attain the equality.
scientific article; zbMATH DE number 3987315