Title: Semiextensions and Circuit Double Covers

Abstract: If G is a cubic graph and C is a circuit 
in G, we will call a circuit D in G a "semiextension" of C 
if (i) D is different from C, (ii) D intersects C, and
(iii) for each vertex x of V(C)\V(D), if P is a minimal
nontrivial path in G from x to some vertex (call it y) on 
either C or D, then there is also a path Q from x to y, such 
that all edges of Q belong to the symmetric difference of 
E(C) and E(D). 
	The definition is motivated by a previous and failed 
approach by Robertson and Seymour to the Circuit Double 
Cover Conjecture (CDCC). We propose to conjecture that a 
semiextension of C always exists, except when the obvious 
obstacles exist. Furthermore, we show that the truth of the 
CDCC would follow from this conjecture. We also note that a 
weakening of our conjecture would imply an unsolved 
conjecture by Sabidussi concerning the existence of a 
circuit decomposition compatible to a given Eulerian trail.