A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex exactly once. A Hamiltonian path that starts and ends at adjacent vertices can be completed by adding one more edge to form a …

Jan 31, 2026 · A Hamiltonian Cycle or Circuit in a graph G is a cycle that visits each vertex of G exactly once and returns to the starting vertex. If a graph has a Hamiltonian cycle, it's a Hamiltonian graph; …

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).

Lecture 22: Hamiltonian Cycles and Paths In this lecture, we discuss the notions of Hamiltonian cycles and paths in the context of both undirected and directed graphs.

The Hamiltonian cycle problem is similar to the Hamiltonian path problem, except it asks if a given graph contains a Hamiltonian cycle. This problem may also specify the start of the cycle.

This is simply finding the Hamilton circuit in a complete graph that has the smallest overall weight. There are several different algorithms that can be used to solve this type of problem.

Hamiltonian Cycle: Today we consider the Hamiltonian cycle problem in directed graphs. Given a digraph G = (V, E), the question is whether there exists a simple cycle that visits all the vertices.

May 27, 2025 · Hamiltonian Cycles are a fundamental concept in Discrete Mathematics, named after the mathematician William Rowan Hamilton. In this article, we will explore the definition, properties, and …

A Hamiltonian path, also called a Hamilton path, is a graph path between two vertices of a graph that visits each vertex exactly once. If a Hamiltonian path exists whose endpoints are adjacent, then the …

A Hamiltonian Cycle or Circuit is a path in a graph that visits every vertex exactly once and returns to the starting vertex, forming a closed loop. A graph is said to be a Hamiltonian graph only when it …