Graph Theory Questions Medium
A Hamiltonian cycle in a graph is a cycle that visits every vertex exactly once, except for the starting and ending vertex which are the same. In other words, it is a closed path in the graph that passes through every vertex exactly once, returning to the starting vertex. This concept is named after Sir William Rowan Hamilton, an Irish mathematician who first studied such cycles. Hamiltonian cycles are important in graph theory as they provide a way to traverse a graph in a specific manner, and their existence or absence in a graph can have significant implications in various applications such as optimization problems and network routing.