(Peer-Reviewed) Surviving rate of graphs and Firefighter Problem
Weifan WANG 王维凡, Jiangxu KONG 孔将旭
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
中国 金华 浙江师范大学数学系
Abstract
The Firefighter Problem on a graph can be viewed as a simplified model of the spread of contagion, fire, rumor, computer virus, etc. The fire breaks out at one or more vertices in a graph at the first round, and the fire-fighter chooses some vertices to protect. The fire spreads to all non-protected neighbors at the beginning of each time-step. The process stops when the fire can no longer spread.
The Firefighter Problem has attracted considerable attention since it was introduced in 1995. In this paper we provide a survey on recent research progress of this field, including algorithms and complexity, Fire-fighter Problem for special graphs (finite and infinite) and digraphs, surviving rate and burning number of graphs. We also collect some open problems and possible research subjects.
High-speed and large-capacity visible light communication for 6G: advances and perspectives
Nan Chi, Zhilan Lu, Fujie Li, Haoyu Zhang, Yunkai Wang, Xinyi Liu, Zhiwu Chen, Zhe Feng, Zhuoran Hu, Zhixue He, Ziwei Li, Chao Shen, Junwen Zhang
Opto-Electronic Technology
2026-03-20
Holotomography-driven learning unlocks in-silico staining of single cells in flow cytometry by avoiding fluorescence co-registration
Daniele Pirone, Giusy Giugliano, Michela Schiavo, Annalaura Montella, Martina Mugnano, Vincenza Cerbone, Maddalena Raia, Giulia Scalia Ivana Kurelac, Diego Luis Medina, Lisa Miccio Mario Capasso, Achille Iolascon, Pasquale Memmolo, Pietro Ferraro
Opto-Electronic Science
2026-02-25
A hybrid integrated high-precision tunable semiconductor laser
Yiran Zhu, Botao Fu, Zhiwei Fang, Qiyue Hu, Jianping Yu, Yunpeng Song, Yu Ma, Min Wang, Kunpeng Jia, Zhenda Xie, Ya Cheng
Opto-Electronic Advances
2026-02-12
Millisecond-level electrically switchable metalens for adaptive rotational depth mapping and diffraction-limited imaging
Yeseul Kim, Jihae Lee, Won-Sik Kim, Hyeonsu Heo, Dongmin Jeon, Beomha Yang, Xiaotong Li, Harit Keawmuang, Shiqi Hu, Young-Ki Kim, Trevon Badloe, Junsuk Rho
Opto-Electronic Advances
2026-02-12
