Cycle double covers and the semi-Kotzig frame

In this paper, we show that a cubic graph G has a circuit double cover if it has a semi-Kotzig frame with at most one non-circuit component. Our result generalizes some results of Goddyn [L.A. Goddyn, Cycle covers of graphs, Ph.D. Thesis, University of Waterloo, 1988], and Häggkvist and Markström [R. Häggkvist, K. Markström, Cycle double covers and spanning minors I, J. Combin. Theory Ser. B 96 (2006) 183-206].