Work

A note on weak saturation number of trees

Year: 2026

Type: article

Abstract: 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 ∈ [ 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.

Source: Discrete Mathematics

DOI: 10.1016/j.disc.2026.115150

Authors: Wenchong Chen, Xiao-Chuan Liu, Xu Yang

Institutions: Nankai University, Universidade Federal de Pernambuco, Universidade Federal de Alagoas

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,320

OpenAlex ID: W7146947084

FWCI:

Cites: 7

Cited by:

Related to: