Perfect Pseudo-Matchings in Cubic Graphs

Abstract

A M in a cubic graph G is a spanning subgraph of G such that every component of M is isomorphic to $$K_2$$ K 2 or to $$K_{1,3}$$ K 1 , 3 . In view of snarks G with dominating cycle C, this is a natural generalization of perfect matchings since $$G \setminus E(C)$$ G \ 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 $$5-$$ 5 - edge-connected snarks.