Posted: August 26th, 2022

Undirected Hamiltonian Paths

This task continues to discover NP-Completeness and NP-Full issues.
Homework Issues
1. Undirected Hamiltonian Paths (12 pts)
2. Hamiltonian Cycles (12 pts)
three. Making Hamiltonian Paths (11 pts)
four. README (1 level)
Whole: 36 factors
Submitting
Submit your resolution to this task in Gradescope hw12. Please assign every web page to the right drawback and ensure your options are legible.
A submission should additionally embody a README containing the required info.
1 Undirected Hamiltonian Paths
Show that UHAMPATH (from lecture) is NP-Full. Begin with the concepts from class. Make sure that to incorporate all of the required components of the proof as described in lecture.
2 Hamiltonian Cycles
Recall that a cycle in a graph (see Sipser Ch zero) is a path that begins and ends on the similar vertex. Additionally, a Hamiltonian path is a path that touches each vertex within the graph.
Show that the next language is NP-Full.
HCYCLE=G is a directed graph with a Hamiltonian cycle
Make sure that to incorporate all of the required components of the proof.
three Making Hamiltonian Paths
Recall that a Hamiltonian path is a path that touches each vertex within the graph.
Show that the next language is NP-Full.
HMAKE=G is a directed graph that has a Hamiltonian path if okay edges are added to it
Make sure that to incorporate all of the required components of the proof.

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