What is 3-symmetric drawing of graph

Question

i have searched through internet, but found only paid articles. Need to understand how Petersen graph can be contracted to K33, it says what through deleting the central vertex of 3-symmetric drawig. But what is 3-symmetric drawing?

Answer 1

Here's a drawing of the Petersen graph with three-fold symmetry. With the aid of the drawing, you should be able to find the needed contraction.

It is interesting that the method suggested in your hint, which requires the deletion of a vertex and its three incident edges followed by three contractions, is not the only way to find a $K_{3,3}$ minor in the Petersen graph. An alternative requires no vertex deletions and only two edge deletions. If the graph is drawn in the usual way with five-fold symmetry, then the two deleted edges should be parallel to each other. Four contractions will then be needed.

Answer 2

Perhaps this should help. Here is a 3-coloring of the Petersen graph. Now contract so independent sets stay independent...

http://en.wikipedia.org/wiki/File:Petersen_graph_3-coloring.svg

In more detail, contract all blue to the neighboring green, and a pair of reds to get 3 reds and 3 greens...