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graph minimum retraction family

For an original labelled simple undirected graph on1..5 vertices0..n-1, construct ALL smallest induced vertex subsets admitting a graph homomorphism retraction: every edge maps to an original edge and every image vertex is fixed. Return minimum image order, every optimum image vertex list, every full vertex-indexed idempotent edge-preserving map, image count and total map count. Edges must be unique sorted pairs u<v in lexicographic order. Images and maps are lexicographically sorted; arrays.

POST https://datenvertrag.halowerk.com/v1/graph-minimum-retraction-family

Eingaben

Felder des veröffentlichten Eingabeschemas
FeldTypPflichtBeschreibung
ninteger, nullJa
edgesSiehe SchemaJa
claimed_imagesSiehe SchemaJa
Vollständiges Eingabeschema anzeigen
{
  "type": "object",
  "additionalProperties": false,
  "required": [
    "n",
    "edges",
    "claimed_images"
  ],
  "properties": {
    "n": {
      "type": [
        "integer",
        "null"
      ],
      "minimum": 1,
      "maximum": 5
    },
    "edges": {
      "anyOf": [
        {
          "type": "array",
          "maxItems": 10,
          "items": {
            "type": "array",
            "maxItems": 2,
            "items": {
              "type": "integer",
              "minimum": 0,
              "maximum": 4
            },
            "minItems": 2
          }
        },
        {
          "type": "null"
        }
      ]
    },
    "claimed_images": {
      "anyOf": [
        {
          "type": "array",
          "maxItems": 32,
          "items": {
            "type": "object",
            "additionalProperties": false,
            "required": [
              "vertices",
              "retractions"
            ],
            "properties": {
              "vertices": {
                "type": "array",
                "maxItems": 5,
                "items": {
                  "type": "integer",
                  "minimum": 0,
                  "maximum": 4
                },
                "minItems": 1
              },
              "retractions": {
                "type": "array",
                "maxItems": 128,
                "items": {
                  "type": "array",
                  "maxItems": 5,
                  "items": {
                    "type": "integer",
                    "minimum": 0,
                    "maximum": 4
                  },
                  "minItems": 1
                }
              }
            }
          }
        },
        {
          "type": "null"
        }
      ]
    }
  }
}

Originalschema öffnen

Veröffentlichtes Eingabebeispiel

{
  "n": 5,
  "edges": [
    [
      0,
      1
    ],
    [
      0,
      4
    ],
    [
      1,
      2
    ],
    [
      2,
      3
    ],
    [
      3,
      4
    ]
  ],
  "claimed_images": [
    {
      "vertices": [
        0,
        1,
        2,
        3,
        4
      ],
      "retractions": [
        [
          0,
          1,
          2,
          3,
          4
        ]
      ]
    }
  ]
}

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Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.

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