Counting Contours on Trees
  We calculate the exact number of contours of size $n$ containing a fixed vertex in $d$-ary trees and provide sharp estimates for this number for more general trees. We also obtain a characterization of the locally finite trees with infinitely many contours of the same size containing a fixed vertex. 
Noga Alon, Rodrigo Bissacot and Eric Ossami Endo
math.CO