Reconfiguring Hamiltonian Cycles in L-Shaped Grid Graphs

2019 ◽  
pp. 325-337
Author(s):  
Rahnuma Islam Nishat ◽  
Sue Whitesides
Keyword(s):  
Hamiltonian Cycles ◽  
Grid Graphs

scholarly journals A Matrix Method for Counting Hamiltonian Cycles on Grid Graphs

1994 ◽  
Vol 15 (3) ◽  
pp. 277-283 ◽  
Author(s):  
Y.H.Harris Kwong ◽  
D.G. Rogers
Keyword(s):  
Matrix Method ◽  
Hamiltonian Cycles ◽  
Grid Graphs

scholarly journals Enumerating Hamiltonian Cycles

10.37236/4510 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Ville H. Pettersson
Keyword(s):  
Dynamic Programming ◽  
Three Dimensional ◽  
Programming Method ◽  
Hamiltonian Cycles ◽  
Dynamic Programming Method ◽  
Hamiltonian Paths ◽  
Grid Graphs ◽  
Triangular Grids ◽  
Arbitrary Graphs

A dynamic programming method for enumerating hamiltonian cycles in arbitrary graphs is presented. The method is applied to grid graphs, king's graphs, triangular grids, and three-dimensional grid graphs, and results are obtained for larger cases than previously published. The approach can easily be modified to enumerate hamiltonian paths and other similar structures.

scholarly journals Some new characterizations of Hamiltonian cycles in triangular grid graphs

2016 ◽  
Vol 201 ◽  
pp. 1-13
Author(s):  
Olga Bodroža-Pantić ◽  
Harris Kwong ◽  
Milan Pantić
Keyword(s):  
Hamiltonian Cycles ◽  
Triangular Grid ◽  
Grid Graphs

Hamiltonicity of a class of toroidal graphs

2020 ◽  
Vol 70 (2) ◽  
pp. 497-503
Author(s):  
Dipendu Maity ◽  
Ashish Kumar Upadhyay
Keyword(s):  
Connected Graph ◽  
Hamiltonian Cycle ◽  
Partial Solution ◽  
The Other ◽  
Hamiltonian Cycles ◽  
The Face ◽  
Toroidal Graphs

Abstract If the face-cycles at all the vertices in a map are of same type then the map is said to be a semi-equivelar map. There are eleven types of semi-equivelar maps on the torus. In 1972 Altshuler has presented a study of Hamiltonian cycles in semi-equivelar maps of three types {36}, {44} and {63} on the torus. In this article we study Hamiltonicity of semi-equivelar maps of the other eight types {33, 42}, {32, 41, 31, 41}, {31, 61, 31, 61}, {34, 61}, {41, 82}, {31, 122}, {41, 61, 121} and {31, 41, 61, 41} on the torus. This gives a partial solution to the well known Conjecture that every 4-connected graph on the torus has a Hamiltonian cycle.

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 Hamiltonian Cycles in Strong Products of Graphs

1979 ◽  
Vol 22 (3) ◽  
pp. 305-309 ◽  
Author(s):  
J. C. Bermond ◽  
A. Germa ◽  
M. C. Heydemann
Keyword(s):  
Connected Graph ◽  
Hamiltonian Cycles ◽  
Strong Product

Abstract. Let denote the graph (k times) where is the strong product of the two graphs G and H. In this paper we prove the conjecture of J. Zaks [3]: For every connected graph G with at least two vertices there exists an integer k = k(G) for which the graph is hamiltonian.

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