Maximal independent sets and separating covers

Details Maximal independent sets and separating covers Maximal independent sets and separating covers

2009-11-21

arxiv.org/abs/0911.4204v2

Mathematics

Combinatorics

To appear in the Monthly

Scientific paper

In 1973, Katona raised the problem of determining the maximum number of subsets in a separating cover on n elements. The answer to Katona's question turns out to be the inverse to the answer to a much simpler question: what is the largest integer which is the product of positive integers with sum n? We give a combinatorial explanation for this relationship, via Moon and Moser's answer to a question of Erdos: how many maximal independent sets can a graph on n vertices have? We conclude by showing how Moon and Moser's solution also sheds light on a problem of Mahler and Popken's about the complexity of integers.

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