A Note on the Strong 2-Cover Conjecture for Graphs Without \(K_5\) Minors

In [J. of Combinatorial Theory (B),40(1986),229-230], Fleischner proved that if \(G\) is a \(2\)-edge-connected planar graph and if \(\mathcal{C}_0 = \{C_1, \ldots, C_k\}\) is a collection of edge-disjoint cycles of \(G\), then \(G\) has a cycle double cover \(\mathcal{C}\) that contains \(\mathcal{C}_0\). In this note, we show that this holds also for graphs that do not have a subgraph contractible to \(K_5\).