# A note on the geodetic number and the Steiner number of AT-free graphs

Wing Kai Hon, Ton Kloks, Hsiang Hsuan Liu, Hung Lung Wang*, Yue Li Wang

*此作品的通信作者

## 摘要

We study two graph parameters, namely the geodetic number and the Steiner number, which are related to the concept of convexity. We show that, in asteroidal triple-free graphs, the Steiner number is greater than or equal to the geodetic number. This answers a question posed by Hernando, Jiang, Mora, Pelayo, and Seara in 2005. Besides, we show that the gap between the two parameters can be arbitrarily large even in unit-interval graphs, a proper subclass of AT-free graphs.

原文 英語 131-135 5 Theoretical Computer Science 854 https://doi.org/10.1016/j.tcs.2020.12.010 已發佈 - 2021 一月 16

• 理論電腦科學
• 電腦科學(全部)