Seminar on Combinatorics
主講者: 王維凡教授(浙江師範大學)
講題: The Surviving Rate of Planar Graphs
時間: 2012-03-16 (Fri.)  14:00 - 15:30
地點: 數學所 722 研討室 (台大院區)
Abstract: Let G be a connected graph with $n\geq 2$ vertices. Let $k\ge 1$ 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 $sn_k(v)$ 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$\rho_k(G)$ of G is defined to be $\Sum_{v\in V(G)}sn_k(v)/n^2$, 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 special graphs such as trees, outerplanar graphs, planar graphs of large girth, d-degenerate graphs, general planar graphs, etc.
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