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In graphs, in which all vertices have an odd degree, the number of Hamiltonian cycles through any fixed edge is always even.

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in Data Structures & Algorithms II by (80.7k points)
In graphs, in which all vertices have an odd degree, the number of Hamiltonian cycles through any fixed edge is always even.

(a) true

(b) false

This question was posed to me in an online quiz.

The origin of the question is Checksum, Complexity Classes & NP Complete Problems in portion Checksum, Complexity Classes & NP Complete Problems of Data Structures & Algorithms II

1 Answer

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Right option is (a) true

Explanation: According to a handshaking lemma, in graphs, in which all vertices have an odd degree, the number of Hamiltonian cycles through any fixed edge is always even.

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