Enrique García-Moreno

*The semiextension conjecture and finding semiextensions *

**Abstract**. We define the concept of a semiextension of a cirtui and outline a proof of the fact that the existence of semiextensions for arbitrary circuits implies the cycle double cover conjecture. We then look at certain circuits of cubic graphs, outline how to find semiextensions of these circuits, and pose some rather interesting questions in this context.