Walks and paths in trees

Abstract

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.

Publication Title

Journal of Graph Theory

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