Abstract
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.
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The authors gratefully acknowledge the support of the Natural Sciences and Engineering Research Council of Canada.
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Nowakowski, R.J., Seyffarth, K. Small Cycle Double Covers of Products II: Categorical and Strong Products with Paths and Cycles. Graphs and Combinatorics 25, 385–400 (2009). https://doi.org/10.1007/s00373-009-0844-x
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DOI: https://doi.org/10.1007/s00373-009-0844-x