  A perfect pseudo-matching M in a cubic graph G is a spanning subgraph of G
such that every component of M is isomorphic to K_2 or to K_1,3.
  In view of snarks G with dominating cycle C, this is a natural generalization
of perfect matchings since G-E(C) is a perfect pseudo-matching.
  Of special interest are such M where the graph G/M is planar because such G
have a cycle double cover. We show that various well known classes of snarks
contain planarizing perfect pseudo-matchings, and that there are at least as
many snarks with planarizing perfect pseudo-matchings as there are cyclically
5-edge-connected snarks.
