Pith Number

pith:CLO3G6A6

pith:2026:CLO3G6A6KFB4KAE45ZQG3PLTKV

not attested not anchored not stored refs pending

Structural description of (bull, house)-free graphs

Chinh T. Hoang, Manoj Belavadi

A structural description of (bull, house)-free graphs shows that (bull, P5)-free graphs have only finitely many k-critical instances for each fixed k.

arxiv:2604.27594 v2 · 2026-04-30 · math.CO

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\usepackage{pith}
\pithnumber{CLO3G6A6KFB4KAE45ZQG3PLTKV}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We give a structural description of (bull, house)-free graphs and also (bull, P_5)-free graphs. Using these structural properties we prove that for any fixed k, the number of k-critical (bull, P_5)-free graphs is finite.

C2weakest assumption

That the claimed structural description correctly captures every (bull, house)-free graph via the decomposition or case analysis used in the proof, without missing cases that would allow infinitely many critical graphs.

C3one line summary

Structural characterizations of (bull, house)-free and (bull, P5)-free graphs enable a finiteness proof for k-critical (bull, P5)-free graphs and a short proof of perfect divisibility.

Receipt and verification

First computed	2026-05-20T00:03:13.100935Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12ddb3781e5143c5009cee606dbd7355534dbe604bd85b21fd6248090952e3f8

Aliases

arxiv: 2604.27594 · arxiv_version: 2604.27594v2 · doi: 10.48550/arxiv.2604.27594 · pith_short_12: CLO3G6A6KFB4 · pith_short_16: CLO3G6A6KFB4KAE4 · pith_short_8: CLO3G6A6

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CLO3G6A6KFB4KAE45ZQG3PLTKV \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 12ddb3781e5143c5009cee606dbd7355534dbe604bd85b21fd6248090952e3f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a15101bcc5c7d12f536e1d84297af7719d1b50a7ddabc056a004ac48cb172c02",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-04-30T08:43:57Z",
    "title_canon_sha256": "9bb2c666b706eb6f6182423db86cdbc95bd89174580804f833fca6b4b3b90337"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.27594",
    "kind": "arxiv",
    "version": 2
  }
}