The 2-surviving rate of planar graphs without 6-cycles

Authors:
Weifan Wang;Stephen Finbow;Jiangxu Kong
Affiliations:
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish B2G 2W5, Canada;Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
Venue:
Theoretical Computer Science
Year:
2014

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Abstract

The firefighter problem models the spread of a fire or virus through a network and the k-surviving rate of G, @r"k(G), is the expected proportion of nodes k fire fighters per turn can save. In this paper, we show that if G is a planar graph with at least two vertices and having no 6-cycles, then @r"2(G)185.