Finding Hamiltonian and Longest (s,t)-Paths of C-Shaped Supergrid Graphs in Linear Time

Finding Hamiltonian and Longest (s,t)-Paths of C-Shaped Supergrid Graphs in Linear Time

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A graph is called Hamiltonian connected if it contains a Hamiltonian path between any two distinct vertices.In the past, we proved the Hamiltonian path and cycle problems for general supergrid graphs to be NP-complete.However, they are still open for solid supergrid graphs.

In this paper, first we will verify the REAMER Hamiltonian cycle property of C-shaped supergrid graphs, which are a special case of solid supergrid graphs.Next, we show that C-shaped supergrid graphs are Hamiltonian connected except in a few conditions.For these excluding ORG PSYLLIUM HUSK POWDER conditions of Hamiltonian connectivity, we compute their longest paths.

Then, we design a linear-time algorithm to solve the longest path problem in these graphs.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.