@article{e3b764031c1747a0998a8fad45a1aa94,
title = "Inducibility and universality for trees",
abstract = "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.",
keywords = "graph density, inducibility, Trees",
author = "Timothy Chan and Daniel Kr{\'a}l{\textquoteright} and Bojan Mohar and Wood, {David R}",
note = "Funding Information: †Supported by the European Research Council (ERC) under the European Union{\textquoteright}s Horizon 2020 research and innovation programme (grant agreement No 648509), and by the MUNI Award in Science and Humanities (MUNI/I/1677/2018) of the Grant Agency of Masaryk University. Previous affiliation: Mathematics Institute, DIMAP, and Department of Computer Science, University of Warwick. Funding Information: ‡Supported by the NSERC Discovery Grant R611450 (Canada), and by the Research Project J1-2452 of ARRS (Slovenia). On leave from IMFM, Department of Mathematics, University of Ljubljana. §Supported by the Australian Research Council. Funding Information: Supported by the European Research Council (ERC) under the European Union{\textquoteright}s Horizon 2020 research and innovation programme (grant agreement No 648509). This publication reflects only its authors{\textquoteright} view; the ERC Executive Agency is not responsible for any use that may be made of the information it contains. Supported by the European Research Council (ERC) under the European Union{\textquoteright}s Horizon 2020 research and innovation programme (grant agreement No 648509), and by the MUNI Award in Science and Humanities (MUNI/I/1677/2018) of the Grant Agency of Masaryk University. Previous affiliation: Mathematics Institute, DIMAP, and Department of Computer Science, University of Warwick.‡ Supported by the NSERC Discovery Grant R611450 (Canada), and by the Research Project J1-2452 of ARRS (Slovenia). On leave from IMFM, Department of Mathematics, University of Ljubljana. Supported by the Australian Research Council. Funding Information: ∗Supported by the European Research Council (ERC) under the European Union{\textquoteright}s Horizon 2020 research and innovation programme (grant agreement No 648509). This publication reflects only its authors{\textquoteright} view; the ERC Executive Agency is not responsible for any use that may be made of the information it contains. Publisher Copyright: {\textcopyright} The authors.",
year = "2022",
doi = "10.5070/C62359150",
language = "English",
volume = "2",
journal = "Combinatorial Theory",
issn = "2766-1334",
publisher = "University of California, eScholarship",
number = "3",
}