How many smaller circuits can be a part of a Hamilton circuit?
A)0
B)1
C)2
D)It varies according to the number of vertices of the Hamilton circuit.

Question

Quizplus · Accepted Answer

A Hamilton circuit must visit every vertex exactly once. Therefore, there can only be one circuit that includes all the vertices. If there were smaller circuits within the Hamilton circuit, that would mean some vertices are not part of the smaller circuits and therefore not being visited exactly once, violating the definition of a Hamilton circuit.

How Many Smaller Circuits Can Be a Part of a Hamilton