alice and bob are discussing a graph that has vertices and edges. bob argues that the graph is hamiltonian, while alice says that he's wrong. without knowing anything more about the graph, must one of them be right? if so, who and why, and if not, why not?

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15-12-2022
Mathematics

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alice and bob are discussing a graph that has vertices and edges. bob argues that the graph is hamiltonian, while alice says that he's wrong. without knowing anything more about the graph, must one of them be right? if so, who and why, and if not, why not?

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aamirmajeed5100 aamirmajeed5100 · Answer 1 · 2022-12-22T12:39:01+01:00

No, neither of them has to be right or wrong in this scenario without any additional information about the graph.

This is because a graph can only be classified as a Hamiltonian if it has a Hamiltonian path, which is a path in the graph that visits each vertex exactly once.

Determining whether or not a graph is Hamiltonian is an NP-hard problem, meaning that there is no known efficient algorithm to solve it. Therefore, without having more information about the graph, neither Alice nor Bob can know for sure if it is Hamiltonian or not.

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