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Hamiltonian path & cycle checker

Check whether a graph has a Hamiltonian path (visits every vertex once) or a Hamiltonian cycle (also returns to the start). Enter an edge list, pick directed or undirected, and an exhaustive backtracking search either returns a concrete path and cycle or proves that none exists. Capped at 12 vertices for speed.

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Open Hamiltonian path & cycle checker and you get an answer straight away, with no account to create. Its place is under Discrete maths & graphs; Dijkstra shortest path calculator and Bitwise Calculator answer the questions closest to this one.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Hamiltonian path & cycle checker?

Check whether a graph has a Hamiltonian path (visits every vertex once) or a Hamiltonian cycle (also returns to the start). Enter an edge list, pick directed or undirected, and an exhaustive backtracking search either returns a concrete path and cycle or proves that none exists. Capped at 12 vertices for speed.

What does a concrete case look like?

Cₙ ✓ · K₁,₃ ✗ — the tool shows every step in between, not just the final figure.

When would I actually use this?

Anything modelled as points and connections: a shortest route, a network's capacity, a schedule with dependencies, or a circuit reduced to its logic.

What is the most common mistake?

Assuming a shortest path stays shortest when a weight changes sign. Negative edges break the greedy argument Dijkstra rests on, and the algorithm returns a confident wrong answer rather than an error.

How is Hamiltonian path & cycle checker different from Dijkstra shortest path calculator?

They sit next to each other but answer different questions: Dijkstra shortest path calculator is the one to open when you need it to enter a weighted graph as edges ("A, B, 4" per line) and a source node: Dijkstra's algorithm returns the shortest distance and the exact path from the source to every reachable vertex. Works for directed or undirected graphs, accepts many edge formats, and flags unreachable vertices — ideal for routing, networks and pathfinding. Pick whichever matches what you're starting from — both are free.

Where do the figures come from?

The algorithms are the textbook ones and their results are exact for the graph you enter. What varies is cost: several of these problems have no known efficient solution, so large inputs are answered by heuristic and the tool says when that is the case.

Further reading

All guides →
GuideLife Path: Two Methods, and One Date in Seven DisagreesAdd the digits of the whole date, or reduce day, month and year first and then add: two textbook methods for the same life path. Over the 46,021 dates from 1900 to 2025 they give different answers 6,398 times — 13.90 %. Every single disagreement is about a master number.How-toHow to Calculate Your Life Path Number (Step by Step)The life path number reduces your full birth date to a single digit. Here is the exact method, the two rules people get wrong, and what the tradition says each number means.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerFibonacci and the Golden RatioThe Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.ExplainerWhat Is a Z-Score? Standard Deviations Above the MeanA z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.