A Splitter for Graphs with No Petersen Family Minor

The Petersen family consists of the seven graphs that can be obtained from the Petersen Graph byYΔ- andΔY-exchanges. A splitter for a family of graphs is a maximal 3-connected graph in the family. In this paper, a previously studied graph,Q13, 3, is shown to be a splitter for the set of all graphs with no Petersen family minor. Moreover,Q13, 3is a splitter for the family of graphs with noK6-minor, as well as for the family of graphs with no Petersen minor.