Hamiltonian paths visit vertex exactly from "summary" of Introduction to Graph Theory by Douglas Brent West
A Hamiltonian path in a graph is a path that visits each vertex exactly once. This means that the path must include every vertex in the graph exactly once, without revisiting any vertex. In other words, a Hamiltonian path is a way to traverse the graph in such a way that every vertex is included in the path exactly once. For example, consider a graph with four vertices A, B, C, and D. A Hamiltonian path in this graph would be a path that starts at one vertex, visits each of the other three vertices exactly once, and ends at the last vertex. In this case, there would be exactly 3! = 6 different Hamiltonian paths i...
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