For hypergraphs, the paper gives faster algorithms for k-weak maximal independent sets and a new (alpha,beta)-independent set variant, plus lower bounds in rank and degree.
Improved distributed lower bounds for mis and bounded (out-) degree dominating sets in trees
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Distributed weak independent sets in hypergraphs: Upper and lower bounds
For hypergraphs, the paper gives faster algorithms for k-weak maximal independent sets and a new (alpha,beta)-independent set variant, plus lower bounds in rank and degree.