Abstract
In this paper, the set of chain recurrent points of monotone maps on graphs is investigated. A compact metric space X has the CR-Pm property provided that for each monotone self-mapping f of X,
, where
and
are the sets of periodic points and chain recurrent points of f, respectively. We show that a local dendrite X has the CR-Pm property if and only if X is a dendrite containing neither the infinite star nor the dendrite
.