Leaf to leaf path lengths in trees of given degree sequence
Abstract
For a tree T , let l p ( T ) be the number of different lengths of leaf to leaf paths in T . For a degree sequence s of a tree, let rad ( s ) be the minimum radius of a tree with degree sequence s . Recently, Di Braccio, Katsamaktsis, Ma, Malekshahian, and Zhao provided a lower bound on l p ( T ) in terms of the number of leaves and the maximum degree of T , answering a related question posed by Narins, Pokrovskiy, and Szabó. Here we show l p ( T ) ≥ rad ( s ) − log 2 ( rad ( s ) ) for a tree T with no vertex of degree 2 and degree sequence s , and discuss possible improvements and variants.
Fields of Study & Subjects
Graph theory and applications
Advanced Graph Theory Research
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Discrete Mathematics
- Volume
- 349
- Issue
- 9
- Pages
- 115086–115086
- Publication date
- 9 March 2026
- Language
- EN