Bipartite coloring check

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

Check a complete 0/1 coloring witness for graph bipartiteness and report the first certificate discrepancy.

Use when you need to: check bipartite coloring witness · validate graph two-color certificate · verify a graph is bipartite.

Decide before calling

Read the versioned contract and the supported scope below. Reuse bipartite-coloring-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 bipartite-coloring-check@1.0.0 for check bipartite coloring witness. 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 bipartite coloring witness
• validate graph two-color certificate
• verify a graph is bipartite
• find first invalid bipartite edge
• check zero one vertex coloring
• audit two-colorability witness

Not supported

• finding a bipartition
• returning an odd cycle
• repairing a two-color witness

Behavior

• colors is an index-aligned total certificate whose only admitted values are integers 0 and 1; null denotes an explicitly missing witness value.
• Edges are inspected in supplied order and must join opposite values; duplicates remain significant and a self-loop conflicts.
• A valid 0/1 coloring certifies bipartiteness; equivalently, a graph is bipartite exactly when it has no odd cycle.
• Every verdict names Diestel Graph Theory 5th ed. (2017), sections 1.6 and 5.2.
• Coverage discrepancies precede edge discrepancies; neither disconnected components nor isolated vertices receive inferred colors.

Input

• vertex_count (integer, required): min 0; max 10000
• edges (array of object, required): max items 50000
• colors (array of integer or null, required): max items 10000; each min 0; each max 1

Output

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

Limits

• max vertices: 10000
• max edges: 50000

Example

Request input:

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

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": "bipartite-coloring-check",
  "version": "1.0.0",
  "input": {
    "vertex_count": 4,
    "edges": [
      {
        "from": 0,
        "to": 1
      },
      {
        "from": 1,
        "to": 2
      },
      {
        "from": 2,
        "to": 3
      }
    ],
    "colors": [
      0,
      1,
      0,
      1
    ]
  }
}

HTTP (no key)

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

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

CLI

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

Get the client at /clients/cli/.

Related tools

• 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.
• 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.
• Chromatic certificate check: Check a claim chi(G) = k: a proper k-colouring plus a clique or bounded exhaustive proof; returns the first discrepancy.
• Graph clique check: Check that listed nodes form a clique (optionally maximal, of a minimum size); returns the first missing edge.