Talk:Edge contraction

Some modifications

This page should clarify the effect of contracting in the presence of loops and multiple edges. 'Vertex contraction' is more commonly called 'vertex identification'. I will make these changes Luis Goddyn (talk) 20:28, 22 January 2009 (UTC)

not quite right..

In graph theory, an edge contraction is an operation which removes an edge from a graph while simultaneously merging together the two vertices it used to connect. All other edges incident to either of the two vertices become incident to the single merged vertex. More generally, one can contract a set of edges by contracting each of them individually in any order. An edge contraction may result in a graph with loops or multiple edges, which are sometimes deleted (as in the diagram) in order to keep within the class of simple graphs. Edge contraction is a fundamental operation in the theory of graph minors.

Loops can't result if the edge is removed before merging the two vertices. McKay (talk) 06:03, 29 March 2009 (UTC)

Actually they can. I can see two possible ways to get loops. If you start with a multgraph and contract on one of the multiedges you'll get a loop (I didn't see any restriction to simple graphs in the definition) or, and I think this was what was meant, if you repeatedly contract you get loops (contract on all the edges of a spanning tree and you'll get a blossom). Bill Cherowitzo (talk) 18:39, 15 June 2014 (UTC)