Importance: High ✭✭✭
Keywords: cycle cover
Recomm. for undergrads: yes
Prize: 50 Euro
Posted by: arthur
on: August 3rd, 2010
Conjecture   Let $ C $ be a circuit in a bridgeless cubic graph $ G $. Then there is a five cycle double cover of $ G $ such that $ C $ is a subgraph of one of these five cycles.

A cycle in $ G $ is meant to be a $ 2 $-regular subgraph of $ G $ . A five cycle double cover of $ G $ is a set of five cycles of $ G $ such that every edge of $ G $ is contained in exactly two of these cycles.

This conjecture is a combination and thus strengthening of the $ 5 $-cycle double cover conjecture and the strong cycle double cover conjecture.


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