A Note on the Strong 2-Cover Conjecture for Graphs Without $K_5$ Minors

Abstract

In [J. of Combinatorial Theory (B),40(1986),229-230], Fleischner proved that if $G$ is a $2$-edge-connected planar graph and if ${\mathcal{C}}_0=\{C_1,\dots ,C_k\}$ 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 $K_5$.