Abstract
The strong cycle double cover conjecture states that for every circuit C of a bridgeless cubic graph G, there is a cycle double cover of G which contains C. We conjecture that there is even a 5-cycle double cover S of G which contains C, i.e. C is a subgraph of one of the five 2-regular subgraphs of S. We prove a necessary and sufficient condition for a 2-regular subgraph to be contained in a 5-cycle double cover of G.
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A. Hoffmann-Ostenhof supported by the FWF project P20543.
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Hoffmann-Ostenhof, A. A Note on 5-Cycle Double Covers. Graphs and Combinatorics 29, 977–979 (2013). https://doi.org/10.1007/s00373-012-1169-8
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DOI: https://doi.org/10.1007/s00373-012-1169-8