Bipartizing matchings and Sabidussi's compatibility conjecture (Q1349078)

In a cubic graph \(G\), with dominating cycle \(C\), a matching \(M\) is called bipartizing if \(M \cap E(C) = \emptyset\), \(M\) covers all of \(V(G)-V(C)\), and \(G-M\) is homeomorphic to a cubic bipartite graph. The author shows that if \(G\) has two disjoint bipartizing matchings, then \(G\) has a cycle double cover \(S\) with \(C \in S\).