Hamiltonian circuit problem example. He . Example 16. Problem Statement Given an undirected graph, the task is to determine whether the graph contains a Hamiltonian cycle or not. 3a. , closed loop) through a graph that visits each node exactly once . Hamiltonian Path and Hamiltonian Circuit- Hamiltonian path is a path in a connected graph that contains all the vertices of the graph. Explore the difference between the Hamiltonian path and Hamiltonian circuit with different examples. One Hamiltonian circuit is shown on the graph below. With Hamiltonian circuits, our focus will not be on existence, but on the question of optimization; given a graph where the edges have weights, can we find the optimal Hamiltonian circuit; the one with lowest total weight. HAMILTONIAN CIRCUIT PROBLEM As our next example, let us consider the problem of finding a Hamiltonian circuit in the graph of Figure 11. He Output: whether G contains a Hamiltonian cycle Algorithm for Hamiltonian Cycle Problem: Enumerate all possible permutations, and check if it corresponds to a Hamiltonian Cycle Running time: O(n!m) = 2O(nlg n) Better algorithm: 2O(n) Far away from polynomial time HC is NP-hard: it is unlikely that it can be solved in polynomial time. There are several other Hamiltonian circuits possible on this graph. Sep 4, 2019 · A Hamiltonian cycle, also called a Hamiltonian circuit, Hamilton cycle, or Hamilton circuit, is a graph cycle (i. Jul 26, 2025 · Hamiltonian Paths have applications in various fields, such as finding optimal routes in transportation networks, circuit design, and graph theory research. 1. Examples of TSP situations are package deliveries, fabricating circuit boards, scheduling jobs on a machine and running errands around town. The first component of our future solution, if it exists, is a first 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. 3b). Notice that the circuit only has to visit every vertex once; it does not need to use every edge. This problem is called the Traveling salesman problem (TSP) because the question can be framed like this: Suppose a salesman needs to give sales pitches in four cities. Hamiltonian Circuits and the Traveling Salesman Problem In the last section, we considered optimizing a walking route for a postal carrier. This comprehensive overview provides a detailed understanding of Hamiltonian circuits, covering their definition, significance, properties, algorithms, and applications. How is this different than the requirements of a package delivery driver? Jan 11, 2025 · A Hamiltonian circuit, often referred to as a Hamiltonian cycle, is a fundamental concept in graph theory with a wide range of applications. Def. The Traveling Salesman Problem (TSP) is any problem where you must visit every vertex of a weighted graph once and only once, and then end up back at the starting vertex. A graph is said to be a Hamiltonian graph only when it contains a hamiltonian cycle, otherwise, it is called non-Hamiltonian graph. e. May 19, 2025 · In this article, we explore Hamiltonian circuits in depth: their definitions, fundamental theorems related to them, illustrative examples, proof strategies, and typical issues encountered while solving such problems. Hamiltonian Graph Examples. Without loss of generality, we can assume that if a Hamiltonian circuit exists, it starts at vertex a. Nov 21, 2023 · Learn what the Hamiltonian path and Hamiltonian circuit are. Accordingly, we make vertex a the root of the state-space tree (Figure 11. qyy sspnh bmz kmcjv dhvai kwhcd yrl fbve gnfqii uobqh