Coloring count check

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

Check a proper indexed coloring and an exact canonical-decimal claim for its number of distinct colors.

Use when you need to: check claimed coloring count · validate number of colors used · verify coloring and distinct color total.

Decide before calling

Read the versioned contract and the supported scope below. Reuse coloring-count-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-count-check@1.0.0 for check claimed coloring count. 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 claimed coloring count
• validate number of colors used
• verify coloring and distinct color total
• check exact graph color count claim
• audit a coloring count certificate
• compare claimed count with used colors

Not supported

• computing the chromatic number
• finding a smaller coloring
• renaming or repairing colors

Behavior

• The supplied assignment must first be a proper total coloring under the same indexed-graph rules as coloring-validity-check.
• claimed_count uses canonical ASCII decimal grammar 0 or [1-9][0-9]*; arithmetic is exact because its bounded value is converted only after grammar checking.
• Distinct colors are exact string values, counted by a prototype-safe Set; null is not a color.
• Every verdict names Diestel Graph Theory 5th ed. (2017), sections 1.6 and 5.2.
• Discrepancies are ordered by vertex coverage, then supplied edge index, then the count comparison.

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
• claimed_count (string, required): max length 5; pattern ^(0|[1-9][0-9]*)$

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": 4,
  "edges": [
    {
      "from": 0,
      "to": 1
    },
    {
      "from": 2,
      "to": 3
    }
  ],
  "colors": [
    "a",
    "b",
    "a",
    "b"
  ],
  "claimed_count": "2"
}

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-count-check",
  "version": "1.0.0",
  "input": {
    "vertex_count": 4,
    "edges": [
      {
        "from": 0,
        "to": 1
      },
      {
        "from": 2,
        "to": 3
      }
    ],
    "colors": [
      "a",
      "b",
      "a",
      "b"
    ],
    "claimed_count": "2"
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/coloring-count-check/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"vertex_count":4,"edges":[{"from":0,"to":1},{"from":2,"to":3}],"colors":["a","b","a","b"],"claimed_count":"2"}'

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

CLI

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

Get the client at /clients/cli/.

Related tools

• Chromatic certificate check: Check a claim chi(G) = k: a proper k-colouring plus a clique or bounded exhaustive proof; returns the first discrepancy.
• Bipartite coloring check: Check a complete 0/1 coloring witness for graph bipartiteness and report the first certificate discrepancy.
• Coloring validity check: Check an indexed graph coloring certificate and report the first uncovered vertex or monochromatic edge.
• Graph coloring check: Check that a node colouring of an undirected graph is proper (and within k colours); returns the first conflict.
• Linear residual check: Check a claimed residual r = b - A x (per component and/or its max norm) exactly for an approximate solution x.
• Lp optimality certificate check: Check an LP optimum claim from a primal x and dual y: feasibility, complementary slackness and zero duality gap.