scholarly journals Approximating the longest paths in grid graphs

2011 ◽  
Vol 412 (39) ◽  
pp. 5340-5350 ◽  
Author(s):  
Wen-Qi Zhang ◽  
Yong-Jin Liu
Keyword(s):  
Grid Graphs ◽  
Longest Paths

scholarly journals Peg Solitaire on Cartesian Products of Graphs

2021 ◽  
Vol 37 (3) ◽  
pp. 907-917
Author(s):  
Martin Kreh ◽  
Jan-Hendrik de Wiljes
Keyword(s):  
Cartesian Product ◽  
Cartesian Products ◽  
Connected Graphs ◽  
Grid Graphs ◽  
Cartesian Products Of Graphs

AbstractIn 2011, Beeler and Hoilman generalized the game of peg solitaire to arbitrary connected graphs. In the same article, the authors proved some results on the solvability of Cartesian products, given solvable or distance 2-solvable graphs. We extend these results to Cartesian products of certain unsolvable graphs. In particular, we prove that ladders and grid graphs are solvable and, further, even the Cartesian product of two stars, which in a sense are the “most” unsolvable graphs.

scholarly journals A linear-time algorithm for the longest path problem in rectangular grid graphs

2012 ◽  
Vol 160 (3) ◽  
pp. 210-217 ◽  
Author(s):  
Fatemeh Keshavarz-Kohjerdi ◽  
Alireza Bagheri ◽  
Asghar Asgharian-Sardroud
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Rectangular Grid ◽  
Grid Graphs ◽  
Longest Path ◽  
Longest Path Problem

Lower bounds for strictly fundamental cycle bases in grid graphs

Networks ◽  
2009 ◽  
Vol 53 (2) ◽  
pp. 191-205 ◽  
Author(s):  
Ekkehard Köhler ◽  
Christian Liebchen ◽  
Gregor Wünsch ◽  
Romeo Rizzi
Keyword(s):  
Lower Bounds ◽  
Grid Graphs ◽  
Fundamental Cycle ◽  
Cycle Bases

Routing in grid graphs by cutting planes

1995 ◽  
Vol 41 (3) ◽  
pp. 255-275 ◽  
Author(s):  
Martin Gr�tschel ◽  
Alexander Martin ◽  
Robert Weismantel
Keyword(s):  
Cutting Planes ◽  
Grid Graphs
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