edge-contraction

Given an edge $xy$ of a graph $G$, the graph $G/xy$ is obtained from $G$ by contracting the edge $xy$; that is, to get $G/xy$ we identify the vertices $x$ and $y$ and remove all loops and duplicate edges. A graph $G^{\prime }$ obtained by a sequence of edge-contractions is said to be a contraction of $G$.

Adapted with permission of the author from by Béla Bollobás, published by Springer-Verlag New York, Inc., 1998.