## Vector spaces and the Petersen graph

### Summary

Summary: It is shown that a matching covered graph has an ear decomposition with no more than one double ear if and only if there is no set S of edges such that |S $\cap A$| is even for every alternating circuit A but |S $\cap C$| is odd for some even circuit C. Two proofs are presented. The first uses vector spaces and the second is constructive.

05C70