  For a tree $T$, consider its smallest subtree $T^{\circ}$ containing all
vertices of degree at least $3$. Then the remaining edges of $T$ lie on
disjoint paths each with one endpoint on $T^{\circ}$. We show that the
chromatic symmetric function of $T$ determines the size of $T^{\circ}$, and the
multiset of the lengths of these incident paths. In particular, this
generalizes a proof of Martin, Morin, and Wagner that the chromatic symmetric
function distinguishes spiders.
