Hamiltonian Path vs. Eulerian Path
Below is the table listing the difference between Hamiltonian Path and Eulerian Path:
|
Characteristics |
Hamiltonian Path |
Eulerian Path |
|---|---|---|
|
Definition |
Visits each vertex exactly once |
Visits each edge exactly once |
|
Existence Condition |
NP-complete problem and no simple characterization |
Exists if exactly 0 or 2 vertices have odd degree |
|
Hamiltonian Cycle |
Starts and ends at the same vertex |
Eulerian Circuit: starts and ends at the same vertex |
|
Problem Complexity |
NP-complete |
Polynomial time |
|
Example Graph Types |
TSP (Traveling Salesman Problem) and pathfinding |
Bridges of Königsberg and mail routing |
Both Hamiltonian and Eulerian paths are fundamental concepts in graph theory. Hamiltonian Path focus on visiting vertices, whereas Eulerian Paths focus on traversing edges.
Difference Between Hamiltonian Path and Eulerian Path
The Hamiltonian and Eulerian paths are two significant concepts used to the solve various problems related to the traversal and connectivity of the graphs. Understanding the differences between these two types of the paths is crucial for the designing efficient algorithms and solving the complex graph problems.