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Throughout cell-cycle progression, the expression of multiple transcripts oscillate, and whether these are under the centralized control of the CDK-APC/C proteins or can be driven by a de-centralized transcription factor (TF) cascade is a fundamental question for understanding cell-cycle regulation. In budding yeast, we find that the transcription of nearly all genes, as assessed by RNA-seq or fluorescence microscopy in single cells, is dictated by CDK-APC/C. Three exceptional genes are transcribed in a pulsatile pattern in a variety of CDK-APC/C arrests. Pursuing one of these transcripts, the SIC1 inhibitor of B-type cyclins, we use a combination of mathematical modeling and experimentation to provide evidence that, counter-intuitively, Sic1 provides a failsafe mechanism promoting nuclear division when levels of mitotic cyclins are low.