On direct product cancellation of graphs |
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Authors: | Richard H Hammack |
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Institution: | Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USA |
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Abstract: | The direct product of graphs obeys a limited cancellation property. Lovász proved that if C has an odd cycle then A×C≅B×C if and only if A≅B, but cancellation can fail if C is bipartite. This note investigates the ways cancellation can fail. Given a graph A and a bipartite graph C, we classify the graphs B for which A×C≅B×C. Further, we give exact conditions on A that guarantee A×C≅B×C implies A≅B. Combined with Lovász’s result, this completely characterizes the situations in which cancellation holds or fails. |
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Keywords: | Graph direct product Cancellation |
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