Pith Number

pith:T5B7HCPY

pith:2026:T5B7HCPYIQDZDCR44UCTN6ZZIC

not attested not anchored not stored refs pending

Triangle packings in randomly perturbed graphs

Hong Liu, Lanchao Wang, Xinbu Cheng, Zhifei Yan

A dn-regular graph unioned with random G(n,p) for p above 2d/(1+2d) admits a triangle packing covering all but o(n²) edges with high probability, and the bound is sharp for d at most 1/2.

arxiv:2604.25250 v2 · 2026-04-28 · math.CO

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\usepackage{pith}
\pithnumber{T5B7HCPYIQDZDCR44UCTN6ZZIC}

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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

for every d>0 and every p>2d/(1+2d), if G_d is a dn-regular graph on n vertices, then with high probability the union G_d ∪ G(n,p) contains a triangle packing covering all but o(n²) edges. Moreover, this bound on p is best possible for 0<d≤1/2.

C2weakest assumption

The random graph G(n,p) is generated independently of the fixed dn-regular graph G_d, and the new triangle-weighting lemma for weighted complete graphs applies directly to the edge weights arising in the perturbed graph without further restrictions.

C3one line summary

For any dn-regular graph perturbed by G(n,p) with p > 2d/(1+2d), there is whp a triangle packing covering all but o(n²) edges, and the bound is optimal for 0 < d ≤ 1/2.

Receipt and verification

First computed	2026-06-11T01:09:36.481940Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f43f389f84407918a3ce50536fb39408c403e225b4b891ce4d4c39006534dc7

Aliases

arxiv: 2604.25250 · arxiv_version: 2604.25250v2 · doi: 10.48550/arxiv.2604.25250 · pith_short_12: T5B7HCPYIQDZ · pith_short_16: T5B7HCPYIQDZDCR4 · pith_short_8: T5B7HCPY

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/T5B7HCPYIQDZDCR44UCTN6ZZIC \
  | 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: 9f43f389f84407918a3ce50536fb39408c403e225b4b891ce4d4c39006534dc7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb897e06870c25989ab382d967175c80b6158a1a39a1e1d679ae58a43f41177b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-04-28T05:57:26Z",
    "title_canon_sha256": "6ca353331535e8c67d4a8319be0768a19dfd627c5e93cc352e656771af13d648"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.25250",
    "kind": "arxiv",
    "version": 2
  }
}