scholarly journals A note on the surviving rate of 1-planar graphs

2017 ◽  
Vol 340 (5) ◽  
pp. 1074-1079 ◽  
Author(s):  
Jiangxu Kong ◽  
Lianzhu Zhang
Keyword(s):  
Planar Graphs ◽  
Surviving Rate

scholarly journals The surviving rate of planar graphs

2012 ◽  
Vol 416 ◽  
pp. 65-70 ◽  
Author(s):  
Jiangxu Kong ◽  
Weifan Wang ◽  
Xuding Zhu
Keyword(s):  
Planar Graphs ◽  
Surviving Rate

Structural properties and surviving rate of planar graphs

2014 ◽  
Vol 06 (04) ◽  
pp. 1450052 ◽  
Author(s):  
Jiangxu Kong ◽  
Lianzhu Zhang ◽  
Weifan Wang
Keyword(s):  
Structural Properties ◽  
Connected Graph ◽  
Planar Graphs ◽  
Time Interval ◽  
Average Proportion ◽  
Surviving Rate

Let G be a connected graph. Suppose that a fire breaks out at some vertex. 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 ρk(G) of G is the average proportion of saved vertices, if the starting vertex of the fire is chosen uniformly at random. A graph G is called k-good if there is a constant c > 0 such that ρk(G) ≥ c. We study structural properties of planar graphs and show that planar graphs are 3-good.

scholarly journals The 2-surviving rate of planar graphs without 4-cycles

2012 ◽  
Vol 457 ◽  
pp. 158-165 ◽  
Author(s):  
Weifan Wang ◽  
Jiangxu Kong ◽  
Lianzhu Zhang
Keyword(s):  
Planar Graphs ◽  
Surviving Rate

The 2-surviving rate of planar graphs without 5-cycles

2015 ◽  
Vol 31 (4) ◽  
pp. 1479-1492 ◽  
Author(s):  
Tingting Wu ◽  
Jiangxu Kong ◽  
Weifan Wang
Keyword(s):  
Planar Graphs ◽  
Surviving Rate

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

2014 ◽  
Vol 518 ◽  
pp. 22-31 ◽  
Author(s):  
Weifan Wang ◽  
Stephen Finbow ◽  
Jiangxu Kong
Keyword(s):  
Planar Graphs ◽  
Surviving Rate

Acute Constraints in Straight-Line Drawings of Planar Graphs

2019 ◽  
Vol E102.A (9) ◽  
pp. 994-1001
Author(s):  
Akane SETO ◽  
Aleksandar SHURBEVSKI ◽  
Hiroshi NAGAMOCHI ◽  
Peter EADES
Keyword(s):  
Planar Graphs ◽  
Line Drawings ◽  
Straight Line

A Space-Efficient Separator Algorithm for Planar Graphs

2019 ◽  
Vol E102.A (9) ◽  
pp. 1007-1016 ◽  
Author(s):  
Ryo ASHIDA ◽  
Sebastian KUHNERT ◽  
Osamu WATANABE
Keyword(s):  
Planar Graphs
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