2021/02/03 by Timothy F. N. Chan, Daniel Král͏̌, Chan, Timothy F. N. +5
Mathematics · Computer Science · Physics and Astronomy · #Graph theory and applications #Topological and Geometric Data Analysis #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2102.02010
We answer three questions posed by Bubeck and Linial on the limit densities of subtrees in trees. We prove there exist positive ε1 and ε2 such that every tree that is neither a path nor a star has inducibility at most 1-ε1, where the inducibility of a tree T is defined as the maximum limit density of T, and that there are infinitely many trees with inducibility at least ε2. Finally, we construct a universal sequence of trees; that is, a sequence in which the limit density of any tree is positive.