
Cycle Double Covers Containing Predefined 2-Regular Subgraphs
Conjecture Let
be a
-connected cubic graph and let
be a
-regular subgraph such that
is connected. Then
has a cycle double cover which contains
(i.e all cycles of
).








Used definitions in the above conjecture: a "cycle" is a connected 2-regular subgraph, a "cycle double cover" of a graph is a set of cycles of
such that every edge of
is contained in precisely two cycles of the set. This conjecture has been motivated by Theorem 3, respectively, Theorem 4 in www.arxiv.org/abs/1711.10614. A weaker conjecture (Conjecture 14) has been stated in "Snarks with special spanning trees" (see www.arxiv.org/abs/1706.05595).