Small Cycle Double Covers of Products II: Categorical and Strong Products with Paths and Cycles

We continue the study of small cycle double covers of products of graphs that began in [7], concentrating here on the categorical product and the strong product. Under the assumption that G has an SCDC, we show that G × P _m has an SCDC for all m ≠ 3, and that G × C _m has an SCDC for all m ≥ 3. For the strong product we use results about the categorical product and the Cartesian product [7] to show that if G has an SCDC, then so does G ⊠ C _m , m ≥ 5. Some results are also given for G ⊠ P _m , but require additional assumptions about the SCDC of G. The authors gratefully acknowledge the support of the Natural Sciences and Engineering Research Council of Canada.