Intersecting P-free families

We study the problem of determining the size of the largest intersecting P-free
family for a given partially ordered set (poset) P. In particular, we find the exact
size of the largest intersecting B-free family where B is the butterfly poset and
classify the cases of equality. The proof uses a new generalization of the partition
method of Griggs, Li and Lu.

(joint with Gerbner and Methuku)