Every Hist-snark has a cycle double cover containing all outer cycles
Every Hist-snark has a cycle double cover containing all outer cycles
Let a Hist-snark be a snark with a Hist, where a Hist is a spanning tree having only vertices of degree three and one, and the outer cycles are the vertex-disjoint cycles induced by the edges outside the Hist. A cycle double cover is a collection of cycles such that every edge is contained in exactly two cycles. Cycle double-cover conjecture for Hist-snarks. Every Hist-snark has a cycle double cover which contains all outer cycles. This is posed as an open problem about cycle double covers of snarks with special spanning trees; the source gives no resolution.
Sources & referencesView supporting material
Primary source
Arthur Hoffmann-Ostenhof and Thomas Jatschka, “Snarks with special spanning trees”, arXiv:1706.05595 (2018).
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