Coloring validity check

coloring-validity-check · version 1.0.0 · Numbers & math · free, no key needed

Check an indexed graph coloring certificate and report the first uncovered vertex or monochromatic edge.

Use when you need to: check graph coloring validity · validate a vertex color assignment · find first coloring conflict.

Decide before calling

Read the versioned contract and the supported scope below. Reuse coloring-validity-check@1.0.0 when your input, required output and limits match it. Choose another approach for an unsupported operation.

Explain the choice

"I can use coloring-validity-check@1.0.0 for check graph coloring validity. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

Supported

• check graph coloring validity
• validate a vertex color assignment
• find first coloring conflict
• check proper graph coloring certificate
• verify every vertex has a color
• test claimed graph coloring

Not supported

• finding or repairing a coloring
• computing the chromatic number
• accepting endpoint names instead of indices

Behavior

• Vertices are the indices 0 through vertex_count-1; edges are inspected in supplied array order.
• A proper coloring assigns one non-null, non-empty exact Unicode string to every vertex and gives adjacent endpoints unequal strings.
• Color equality is exact JavaScript string equality; no normalization, case folding, trimming, or color renaming occurs.
• Every verdict names Diestel Graph Theory 5th ed. (2017), sections 1.6 and 5.2; duplicates are checked in place and a self-loop necessarily conflicts.
• A false verdict reports coverage discrepancies before edge discrepancies; ties use ascending vertex or edge index.

Input

• vertex_count (integer, required): min 0; max 10000
• edges (array of object, required): max items 50000
• colors (array of string or null, required): max items 10000; each max length 64

Output

• valid (boolean, required)
• reason (string, optional)
• discrepancy (object, optional)
• reference_version (string, required)

Limits

• max vertices: 10000
• max edges: 50000
• max color bytes: 64

Example

Request input:

{
  "vertex_count": 3,
  "edges": [
    {
      "from": 0,
      "to": 1
    },
    {
      "from": 1,
      "to": 2
    }
  ],
  "colors": [
    "red",
    "blue",
    "red"
  ]
}

Response:

{
  "result": {
    "valid": true,
    "reference_version": "Diestel Graph Theory 5th ed. (2017), sections 1.6 and 5.2"
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "coloring-validity-check",
  "version": "1.0.0",
  "input": {
    "vertex_count": 3,
    "edges": [
      {
        "from": 0,
        "to": 1
      },
      {
        "from": 1,
        "to": 2
      }
    ],
    "colors": [
      "red",
      "blue",
      "red"
    ]
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/coloring-validity-check/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"vertex_count":3,"edges":[{"from":0,"to":1},{"from":1,"to":2}],"colors":["red","blue","red"]}'

The machine-readable contract is at /v1/tools/coloring-validity-check/versions/1.0.0.

CLI

node cli.mjs run coloring-validity-check 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Bipartite coloring check: Check a complete 0/1 coloring witness for graph bipartiteness and report the first certificate discrepancy.
• Graph coloring check: Check that a node colouring of an undirected graph is proper (and within k colours); returns the first conflict.
• Network flow feasibility check: Check a claimed s-t flow for capacity bounds and conservation with exact integers; returns the first bad edge or node.
• Coloring count check: Check a proper indexed coloring and an exact canonical-decimal claim for its number of distinct colors.
• Spanning tree structure check: Check that claimed edge IDs form a spanning tree of a graph; reports the first missing, repeated or cyclic edge
• Chromatic certificate check: Check a claim chi(G) = k: a proper k-colouring plus a clique or bounded exhaustive proof; returns the first discrepancy.