Learning a maximum-scored Bayesian network structure with bounded treewidth is rather popular in recent years, as stated in the paper A survey on Bayesian network structure learning from data in 2019. However, I failed to find out any recent research on the structural learning of a maximum-scored Bayesian network with bounded number of parents for each variable(node). D.M. Chickering(1996) formalised this problem as $K$-LEARN where $K$ is the upper bounded for number of parents and proved its NP-Completeness in Learning Bayesian Networks is NP-Complete. Since then, to the best of my knowledge, far less attention is paid to $K$-LEARN in the community(in fact, I couldn't find out any related paper), compared with its popular treewidth-bounded version.
So is $K$-LEARN not considered as a good research topic anymore or it has never been the case? Or I just missed the whole line of research for it since 1996? Any help would be appreciated.
Note: The treewidth of a Bayesian network is defined as the treewidth of its moralised graph, by Elidan and Gould in Learning Bounded Treewidth Bayesian Networks(2008)