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arXiv · 1711.10614

Cycle double covers and non-separating cycles

Arthur Hoffmann-Ostenhof·Cun-Quan Zhang·Zhang Zhang
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Abstract

Which $2$-regular subgraph $R$ of a cubic graph $G$ can be extended to a cycle double cover of $G$? We provide a condition which ensures that every $R$ satisfying this condition is part of a cycle double cover of $G$. As one consequence, we prove that every $2$-connected cubic graph which has a decomposition into a spanning tree and a $2$-regular subgraph $C$ consisting of $k$ circuits with $k\leq 3$, has a cycle double cover containing $C$.

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Arthur Hoffmann-Ostenhof, Cun-Quan Zhang, Zhang Zhang. 2018-08-20. Cycle double covers and non-separating cycles. https://arxiv.org/abs/1711.10614

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