  We generalize the classical single-crossing property to single-crossing
property on trees and obtain new ways to construct Condorcet domains which are
sets of linear orders which possess the property that every profile composed
from those orders have transitive majority relation. We prove that for any tree
there exist profiles that are single-crossing on that tree; moreover, that tree
is minimal in this respect for at least one such profile. Finally, we provide a
polynomial-time algorithm to recognize whether or not a given profile is
single-crossing with respect to some tree. We also show that finding winners
for Chamberlin-Courant rule is polynomial for profiles that are single-crossing
on trees.
