The Surviving Rate of a Graph

主讲教师:王维凡 人气:1212 更新时间: 2017年06月24日
摘要: 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 neighbour on fire. Let snk(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 ρk(G) of G is defied to be P v∈V snk(v)/n2 , which is the average proportion of saved vertices. In this talk, we give a chief survey on this direction and related problems. In particular, we consider the firefighter problems for some graphs such as trees, outerplanar graphs, planar graphs, d-degenerate graphs, etc


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