The Hamiltonicity, Hamiltonian Connectivity, and Longest (s, t)-path of L-shaped Supergrid Graphs
Abstract
Supergrid graphs contain grid graphs and triangular grid graphs as their subgraphs. The Hamiltonian cycle and path problems for general supergrid graphs were known to be NP-complete. A graph is called Hamiltonian if it contains a Hamiltonian cycle, and is said to be Hamiltonian connected if there exists a Hamiltonian path between any two distinct vertices in it. In this paper, we first prove that every L-shaped supergrid graph always contains a Hamiltonian cycle except one trivial condition. We then verify the Hamiltonian connectivity of L-shaped supergrid graphs except few conditions. The Hamiltonicity and Hamiltonian connectivity of L-shaped supergrid graphs can be applied to compute the minimum trace of computerized embroidery machine and 3D printer when a L-like object is printed. Finally, we present a linear-time algorithm to compute the longest (s, t)-path of L-shaped supergrid graph given two distinct vertices s and t.
Keywords
Cite
@article{arxiv.1904.02581,
title = {The Hamiltonicity, Hamiltonian Connectivity, and Longest (s, t)-path of L-shaped Supergrid Graphs},
author = {Fatemeh Keshavarz-Kohjerdi and Ruo-Wei Hung},
journal= {arXiv preprint arXiv:1904.02581},
year = {2019}
}
Comments
A preliminary version of this paper has appeared in: The International MultiConference of Engineers and Computer Scientists 2018 (IMECS 2018), Hong Kong, vol. I, 2018, pp. 117-122