HAMILTONIAN CYCLE Meaning and
Definition
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A Hamiltonian cycle refers to a term used in discrete mathematics and graph theory to describe a closed loop or cycle that visits every vertex of a given undirected graph exactly once. Specifically, a Hamiltonian cycle in a graph refers to a path that starts and ends at the same vertex, with each vertex being visited only once. It is named after the Irish mathematician Sir William Rowan Hamilton, who first introduced the concept in the 19th century.
In order for a graph to possess a Hamiltonian cycle, it must satisfy certain conditions. Firstly, all vertices in the graph must be connected to one another, meaning that there should be an edge connecting every pair of vertices. Additionally, it is essential for the Hamiltonian cycle to be able to traverse through every vertex, without skipping any.
The Hamiltonian cycle is a fundamental concept in graph theory and serves as a tool to analyze and understand various aspects of graph structures. It has numerous applications in areas such as computer science, transportation planning, communication networks, and manufacturing systems. Determining the existence of a Hamiltonian cycle in a graph is challenging, as it is considered an NP-complete problem in computational complexity theory, which implies that no efficient algorithm exists to solve it for large graphs.
Common Misspellings for HAMILTONIAN CYCLE
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Etymology of HAMILTONIAN CYCLE
The word "Hamiltonian cycle" is derived from the name of the Irish mathematician William Rowan Hamilton, who first introduced the concept in the 19th century. Hamilton made significant contributions to the field of graph theory, particularly in the study of paths and circuits in graphs. The term "Hamiltonian cycle" was coined to honor his pioneering work in this area.
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