Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776999 | Discrete Mathematics | 2017 | 6 Pages |
Abstract
For a connected graph G, suppose that a fire breaks out at its vertex and a firefighter starts to protect vertices. At each time interval, the firefighter protects k vertices not yet on fire. At the end of each time interval, the fire spreads to all the unprotected vertices that have a neighbor on fire. The k-surviving rate Ïk(G) of G is defined to be the expected percentage of vertices saved if the fire breaks out at a random vertex. In this note, we consider the surviving rate of 1-planar graphs, and show that every 1-planar graph G has Ï6(G)>1163.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Jiangxu Kong, Lianzhu Zhang,