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Bibliographic Details
Main Authors: Chen, Wenchong, Liu, Xiao-Chuan, Yang, Xu
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2502.15626
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Table of Contents:
  • In this paper, we estimate the weak saturation numbers of trees. As a case study, we examine caterpillars and obtain several tight estimates. In particular, this implies that for any $α\in [1,2]$, there exist caterpillars with $k$ vertices whose weak saturation numbers are of order $k^α$. We call a tree good if its weak saturation number is exactly its edge number minus one. We provide a sufficient condition for a tree to be a good tree. With the additional property that all leaves are at even distances from each other, this condition fully characterizes good trees.