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# 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 *Modern Graph Theory* by Béla Bollobás, published by Springer-Verlag New York, Inc., 1998.

Defines:

contraction

Related:

TheoremOn3ConnectedGraphs

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

05C99*no label found*

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