On paths, stars and wyes in trees
Combinatorics
2016-01-11 v1
Abstract
We further the study of local profiles of trees. Bubeck and Linial showed that the set of 5-profiles contains a certain polytope, namely the convex hull of d-millipedes, and they proved that the segment [0-millipede, 1-millipede] corresponds to a face of the set of 5-profiles. Our main result shows that the segment [1-millipede, 2-millipede] also corresponds to a face. Surprisingly we also show that for d > 3 the segment [d-millipede, (d+1)-millipede] is not a face of the set of 5-profiles. We do so by exhibiting new trees which are generalized millipedes with intriguing patterns for their degree sequence. The plot thickens, and the set of 5-profiles remains a mysterious convex set.
Keywords
Cite
@article{arxiv.1601.01950,
title = {On paths, stars and wyes in trees},
author = {Sébastien Bubeck and Katherine Edwards and Horia Mania and Cathryn Supko},
journal= {arXiv preprint arXiv:1601.01950},
year = {2016}
}
Comments
11 pages, 2 figures