Inducibility and universality for trees
| Authors | |
|---|---|
| Year of publication | 2022 |
| Type | Article in Periodical |
| Magazine / Source | Combinatorial Theory |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.5070/C62359150 |
| Doi | http://dx.doi.org/10.5070/C62359150 |
| Keywords | trees; inducibility; graph density |
| Description | We answer three questions posed by Bubeck and Linial on the limit densities of subtrees in trees. We prove there exist positive e1 and e2 such that every tree that is neither a path nor a star has inducibility at most 1-e1, 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 e2. Finally, we construct a universal sequence of trees; that is, a sequence in which the limit density of any tree is positive. |
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