scholarly journals Metro Maps on Octilinear Grid Graphs

2020 ◽  
Vol 39 (3) ◽  
pp. 357-367
Author(s):  
Hannah Bast ◽  
Patrick Brosi ◽  
Sabine Storandt
Keyword(s):  
Grid Graphs ◽  
Metro Maps

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

scholarly journals From Modernism to Metro Maps: Mondrian, Beck, and Salomon

2017 ◽  
Vol 1 (1) ◽  
Author(s):  
Peter B. Lloyd
Keyword(s):  
Dynamic Equilibrium ◽  
Dynamic Balance ◽  
Computer Software ◽  
Automatic Generation ◽  
Acceptable Quality ◽  
Daunting Task ◽  
London Underground ◽  
Superficial Similarity ◽  
Psychological Force ◽  
Metro Maps

Many people have noted a suggestive parallel between the abstract paintings of Piet Mondrian and the design of metro maps such as Henry Beck’s map of the London Underground. Is this just a superficial similarity or is there some more substantive point of connection? This article speculates that the ‘dynamic equilibrium’, which gave Mondrian’s mature pictures their inimitable psychological force, could also be at work in the most iconic metro maps, such as those of Henry Beck and George Salomon. If so, then the automatic generation of metro maps to an acceptable quality may entail the daunting task of operationalising this dynamic balance and encoding it in computer software. 

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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