Walks and paths in trees
Recently Csikvári [Combinatorica 30(2) 2010, 125-137] proved a conjecture of Nikiforov concerning the number of closed walks on trees. Our aim is to extend this theorem to all walks. In addition, we give a simpler proof of Csikvári's result and answer one of his questions in the negative. Finally we consider an analogous question for paths rather than walks. © 2011 Wiley Periodicals, Inc.
Journal of Graph Theory
Bollobás, B., & Tyomkyn, M. (2012). Walks and paths in trees. Journal of Graph Theory, 70 (1), 54-66. https://doi.org/10.1002/jgt.20600