Journal ArticleDOI
The Hamiltonian connectivity of rectangular supergrid graphs
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In this paper, the authors studied the Hamiltonian connectivity of rectangular supergrid graphs and provided a linear-time algorithm to construct a longest path between any two given vertices in a rectangle supergrid graph.About:
This article is published in Discrete Optimization.The article was published on 2017-11-01. It has received 14 citations till now. The article focuses on the topics: Hamiltonian path problem & Indifference graph.read more
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The Hamiltonicity, Hamiltonian Connectivity, and Longest (s, t)-path of L-shaped Supergrid Graphs
TL;DR: It is proved that every L-shaped supergrid graph always contains a Hamiltonian cycle except one trivial condition, and the Hamiltonicity and Hamiltonian connectivity can be applied to compute the minimum trace of computerized embroidery machine and 3D printer when a L-like object is printed.
Journal ArticleDOI
Linear-time algorithms for finding Hamiltonian and longest (s,t)-paths in C-shaped grid graphs
TL;DR: The necessary conditions for the existence of Hamiltonian cycles and Hamiltonian ( s , t ) -paths in such graphs are given and it is shown that these necessary conditions are also sufficient for a linear-time algorithm to find the longest path in these graphs.
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Finding Hamiltonian and Longest (s, t)-paths of C-shaped Supergrid Graphs in Linear Time
TL;DR: The Hamiltonian connectivity of C-shaped supergrid graphs can be applied to compute the optimal stitching trace of computer embroidery machines, and construct the minimum printing trace of 3D printers with a C-like component being printed.
Proceedings ArticleDOI
The Hamiltonian connectivity of some alphabet supergrid graphs
TL;DR: The results can be used to verify the Hamiltonian connectivity of other alphabet supergrid graphs with similar structure, such as G-, H-, J-, I-, O, P-, T-, S-, and U-alphabetsupergrid graphs.
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Finding Hamiltonian and Longest (s,t)-Paths of C-Shaped Supergrid Graphs in Linear Time
TL;DR: In this paper , it was shown that C-shaped supergrid graphs are Hamiltonian connected, except for a few conditions, and a linear-time algorithm was designed to solve the longest path problem in these graphs.
References
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Book
Graph theory with applications
TL;DR: In this paper, the authors present Graph Theory with Applications: Graph theory with applications, a collection of applications of graph theory in the field of Operational Research and Management. Journal of the Operational research Society: Vol. 28, Volume 28, issue 1, pp. 237-238.
Journal ArticleDOI
Hamilton Paths in Grid Graphs
TL;DR: This work gives necessary and sufficient conditions for the graph to have a Hamilton path between these two nodes, and provides a new, relatively simple, proof of the result that the Euclidean traveling salesman problem is NP-complete.
Hamiltonian Path Problems in the On-line Optimization of Flexible Manufacturing Systems
TL;DR: This thesis computationally compare several on-line heuristics and derive lower bounds on the value obtained by an optimal on--line strategy by analyzing two off--line Combinatorial Optimization problems: the asymmetric Hamiltonian path problem with precedence constraints and the asymmetry of time windows.