The surviving rate of an infected network
Theoretical Computer Science
The Surviving Rate of a Graph for the Firefighter Problem
SIAM Journal on Discrete Mathematics
The surviving rate of an outerplanar graph for the firefighter problem
Theoretical Computer Science
Surviving Rates of Graphs with Bounded Treewidth for the Firefighter Problem
SIAM Journal on Discrete Mathematics
The 2-surviving rate of planar graphs without 4-cycles
Theoretical Computer Science
The 2-surviving rate of planar graphs without 6-cycles
Theoretical Computer Science
A lower bound of the surviving rate of a planar graph with girth at least seven
Journal of Combinatorial Optimization
| Hi-index | 5.23 |
Let G be a connected graph with n=2 vertices. Let k=1 be an integer. Suppose that a fire breaks out at a vertex v of G. 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. Let sn"k(v) denote the maximum number of vertices in G that the firefighter can save when a fire breaks out at vertex v. The k-surviving rate @r"k(G) of G is defined to be @?"v"@?"V"("G")sn"k(v)/n^2, which is the average proportion of saved vertices. In this paper, we show that every planar graph G with minimum degree @d satisfies @r"4(G)311 if @d=5, @r"4(G)319 if @d=4, and @r"4(G)19 if @d@?3. This improves a result in [W. Wang, S. Finbow, P. Wang, The surviving rate of an infected network, Theoret. Comput. Sci. 411 (2010) 3651-3660].