![](/files/happy5.png)
Conjecture Let
be a circuit in a bridgeless cubic graph
. Then there is a five cycle double cover of
such that
is a subgraph of one of these five cycles.
![$ C $](/files/tex/05d3558ef52267cc1af40e658352d98883668ee3.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ C $](/files/tex/05d3558ef52267cc1af40e658352d98883668ee3.png)
A cycle in is meant to be a
-regular subgraph of
. A five cycle double cover of
is a set of five cycles of
such that every edge of
is contained in exactly two of these cycles.
This conjecture is a combination and thus strengthening of the -cycle double cover conjecture and the strong cycle double cover conjecture.
Bibliography
* indicates original appearance(s) of problem.