DeepAI

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

A supergrid graph is a finite vertex-induced subgraph of the infinite graph whose vertex set consists of all points of the plane with integer coordinates and in which two vertices are adjacent if the difference of their x or y coordinates is not larger than 1. The Hamiltonian path (cycle) problem is to determine whether a graph contains a simple path (cycle) in which each vertex of the graph appears exactly once. This problem is NP-complete for general graphs and it is also NP-complete for general supergrid graphs. Despite the many applications of the problem, it is still open for many classes, including solid supergrid graphs and supergrid graphs with some holes. A graph is called Hamiltonian connected if it contains a Hamiltonian path between any two distinct vertices. In this paper, first we will study the Hamiltonian cycle property of C-shaped supergrid graphs, which are a special case of rectangular supergrid graphs with a rectangular hole. Next, we will show that C-shaped supergrid graphs are Hamiltonian connected except few conditions. Finally, we will compute a longest path between two distinct vertices 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.

• 3 publications
• 3 publications
04/04/2019

The Hamiltonicity, Hamiltonian Connectivity, and Longest (s, t)-path of L-shaped Supergrid Graphs

Supergrid graphs contain grid graphs and triangular grid graphs as their...
11/16/2019

The Longest (s, t)-paths of O-shaped Supergrid Graphs

In this paper, we continue the study of the Hamiltonian and longest (s, ...
05/17/2021

Hamiltonian Cycle Problem is in P

In this paper we present the first deterministic polynomial time algorit...
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Generalized Hamiltonian Dynamics and Chaos in Evolutionary Games on Networks

We study the network replicator equation and characterize its fixed poin...
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The embedding is an essential step when calculating on the D-Wave machin...
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A heuristic algorithm for straight-line embedding of a hamiltonian cycle onto a given set of points inside simple polygons

This paper investigated the problem of embedding a simple Hamiltonian Cy...
05/16/2022

The Hamiltonian Path Graph is Connected for Simple s,t Paths in Rectangular Grid Graphs

A simple s,t path P in a rectangular grid graph 𝔾 is a Hamiltonian path ...