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The paper describes a new class of Bayes nets for which inference and structure learning can be done in polynomial time. This is the class of Bayes nets with a bounded vertex cover number. So far, the only other class of Bayes nets for which inference and structure learning is tractable is the class of trees. Hence, this is an important contribution that advances our understanding of tractable probabilistic graphical models. The paper also describes two algorithms to find the best Bayes net structure for a bounded vertex cover k, however it is not clear whether practitioners would want to use those algorithms.