Suppose that the maximum size of a sunflower with no head in a family of 2-sets is r. Then the idea of the matching augmentation algorithm can be used to show that there are integers p and qi and disjoint sets Y and Xi such that:-

• r = p + Σqi

• Y has p elements

• Each Xi has 2qi +1 elements

• The given family consists only of sets with both elements in an Xi and sets with one or both elements in Y.

The maximum size of a sunflower with head of size 1 then limits the sizes of the p and qi. [Each i is supposed to be a suffix.]

]]>Yes it does. So an example would be the sets and . Those form a sunflower with head and petals and .

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