Excluding Minors in Cubic Graphs
Kyriakos Kilakos, F. Bruce Shepherd · Combinatorics Probability Computing · 1996
Let P10\e be the graph obtained by deleting an edge from the Petersen graph. We give a decomposition theorem for cubic graphs with no minor isomorphic to P10\e. The decomposition is used to show that graphs in this class are 3-edge-colourable. We also consider an application to a conjecture due to Grötzsch which states that a planar graph is 3-edge-colourable if and only if it is fractionally 3-edge-colourable.