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 \(G \setminus E(C)\) is a perfect pseudo-matching. Of special interest are such M where 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.
