Bipartizing matchings and Sabidussiʹs compatibility conjecture Original Research Article

In a cubic graph G3 with dominating cycle C, a matching M is called bipartizing if M∩E(C)=∅, M covers all of V(G3)−V(C), and G3−M is homeomorphic to a cubic bipartite graph. In this note it will be shown that if G3 has two disjoint bipartizing matchings, then G3 has a cycle double cover S with C∈S.