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In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex exactly once.
1 Ιαν 1988 · A graph is hamiltonian if it contains a closed cycle passing through every vertex. In this paper we outline the history of hamiltonian graphs from the early studies on the knight's tour problem to Gabriel Dirac's important paper of 1952.
1 Αυγ 2024 · Euler and Hamiltonian paths are fundamental concepts in graph theory, a branch of mathematics that studies the properties and applications of graphs. An Euler path visits every edge of a graph exactly once, while a Hamiltonian path visits every vertex exactly once.
History of the Hamiltonian Cycle. The cycle was named after Sir William Rowan Hamilton who, in 1857, invented a puzzle-game which involved hunting for a Hamiltonian cycle.
A Hamilton circuit is one that passes through each point exactly once but does not, in general, cover all the edges; actually, it covers only two of the three edges that intersect at each vertex. The route shown in heavy lines is one of several possible…
26 Νοε 2024 · A Hamiltonian cycle, also called a Hamiltonian circuit, Hamilton cycle, or Hamilton circuit, is a graph cycle (i.e., closed loop) through a graph that visits each node exactly once (Skiena 1990, p. 196). A graph possessing a Hamiltonian cycle is said to be a Hamiltonian graph.
A Hamiltonian arcuit of an undirected graph G = (V, E) is a simple circuit that includes all the vertices of G. The graph in Figure 11.6 contains several Hamiltonian circuits —for example, 〈1, 4, 5, 6, 3, 2〉 and 〈1, 2, 3, 4, 5, 6〉.
