Random Hamiltonian Cycle Instance Generator

Description

Generate a simple graph containing a shuffled all-vertex cycle and an exact number of extra edges, with a Hamiltonian witness but no uniqueness claim.

A graph uses vertices and edges to represent relationships. Direction, duplicate handling, indexing, and traversal order affect its interpretation; returning a constructed graph together with a witness or calculated answer helps verify an algorithm.

Generate a simple graph containing a shuffled all-vertex cycle and an exact number of extra edges, with a Hamiltonian witness but no uniqueness claim.

When to use this tool

Use this generator to create reproducible hamiltonian cycle instance cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.

How to use the tool and how it works

Supply nodeCount, edgeCount in the field shapes below. Set seed when you need an explicit replay.
Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
Read nodes, edges, cycle. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.

Shuffle nodes into a closed Hamiltonian cycle, plant all cycle edges, and add distinct simple undirected edges to reach edgeCount. Return the cycle with its starting node repeated at the end.^[1]

Input field	Meaning and units	Accepted input
nodeCount	Number of vertices, labeled 0 through nodeCount - 1.	Required. Safe integer; minimum 3; maximum 32.
edgeCount	Exact number of generated edges; feasibility is checked against the selected construction.	Required. Safe integer; minimum 0; maximum 496.
seed	Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed.	Optional. Safe integer.

Output field	Interpretation	Returned shape
nodes	Nodes	Required. Array of Safe integer; minimum 0.; maximum items 32.
edges	Edges	Required. Array of Array of Safe integer; minimum 0.; minimum items 2; maximum items 2.; maximum items 496.
randomness	Replay metadata: source is seed or context; seed is the normalized 32-bit seed or null for a context source.	Required. Object; no unknown keys.
randomness.seed	Optional numeric replay seed; normalization and precedence are explained below.	Required. Safe integer. or Null.
randomness.source	Source	Required. Text; one of "context", "seed".
cycle	Cycle	Required. Array of Safe integer; minimum 0.; minimum items 4; maximum items 33.

An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.

json

{
  "input": {
    "nodeCount": 5,
    "edgeCount": 7,
    "seed": 42
  },
  "output": {
    "nodes": [
      0,
      1,
      2,
      3,
      4
    ],
    "edges": [
      [
        0,
        2
      ],
      [
        0,
        3
      ],
      [
        0,
        4
      ],
      [
        1,
        2
      ],
      [
        1,
        3
      ],
      [
        2,
        3
      ],
      [
        2,
        4
      ]
    ],
    "randomness": {
      "seed": 42,
      "source": "seed"
    },
    "cycle": [
      0,
      4,
      2,
      1,
      3,
      0
    ]
  }
}

Limitations and assumptions

The witness visits every node once before closure but need not be unique. This generates a feasible instance rather than solving arbitrary Hamiltonian-cycle inputs or sampling all such graphs uniformly.
A replay requires the same complete input and implementation. Randomized construction does not guarantee uniform coverage of every feasible output; finite samples can repeat unless a distinct-selection rule is explicitly stated.
The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.

Alternative or Complementary methods

For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.

References

Tool behavior and example: Random Hamiltonian Cycle Instance Generator — tool.io

Similar or alternative tools

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