TITLE: A center of a graph (for example a tree) lies on its longest path
QUESTION [5 upvotes]: Prove a center of a tree (or if not much harder, of any graph) lies on the longest path.
(I encountered this when I was reading an alternative proof for the property :"a tree has at most two centers")

REPLY [2 votes]: You might find these items of interest: http://web.archive.org/web/20100619094433/http://orion.math.iastate.edu/axenovic/Papers/Path-Transversals.pdf and http://www.math.uiuc.edu/~west/openp/pathtran.html