Recently Csikvari [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 Csikvari's result and answer one of his questions in the negative. Finally we consider an analogous question for paths rather than walks. © 2012 Wiley Periodicals, Inc.#R##N##R##N#(Contract grant sponsor: NSF; Contract grant numbers: CCR-0225610; DMS-0505550; W911NF-06-1-0076 (to B. B.).)
['Béla Bollobás', 'Mykhaylo Tyomkyn']
Walks and Paths in Trees