Pith Number

pith:DAKX4PHT

pith:2026:DAKX4PHTS3PI5WWFGGKNK34AJ7

not attested not anchored not stored refs pending

Fractional clique decompositions of dense balanced multipartite graphs

Hengrui Liu, Shikang Yu, Tao Feng

Balanced r-partite graphs with high partite minimum degree admit fractional K_s-decompositions for small enough density deficits depending on r and s.

arxiv:2604.25206 v2 · 2026-04-28 · math.CO

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4 Citations open

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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

if r≥s+2 and the partite minimum degree of G is at least (1-c)n with c≤1/((s-2)(s+1)(s-1)^4), then G has a fractional K_s-decomposition; for r=s+1 the bound is c≤1/(3s^3(s-2)^2) under s-admissibility.

C2weakest assumption

The graphs must be balanced (equal part sizes) and the s-admissibility condition must hold; the association scheme averaging argument assumes the density is high enough for the error terms to be controlled by the given c bounds.

C3one line summary

Balanced r-partite graphs with partite minimum degree at least (1-c)n admit fractional K_s-decompositions for r >= s+1 under explicit c bounds that depend on s and the gap between r and s.

Cited by

1 paper in Pith

On the completion of $\epsilon$-dense partial Latin squares

Receipt and verification

First computed	2026-06-25T01:17:53.503485Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

18157e3cf396de8edac53194d56f804fff2fb2e55699a92056a1c9939723e390

Aliases

arxiv: 2604.25206 · arxiv_version: 2604.25206v2 · doi: 10.48550/arxiv.2604.25206 · pith_short_12: DAKX4PHTS3PI · pith_short_16: DAKX4PHTS3PI5WWF · pith_short_8: DAKX4PHT

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/DAKX4PHTS3PI5WWFGGKNK34AJ7 \
  | 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: 18157e3cf396de8edac53194d56f804fff2fb2e55699a92056a1c9939723e390

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57f3d951c4aa8f707db15bdbcb504ba99b80a415e46fcde4992e4884a2ef6dd8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-04-28T04:23:55Z",
    "title_canon_sha256": "35d481cb58e797e38ccc889f1e2dd96f0936946d0e9be3db59bdfbbcaf916bb5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.25206",
    "kind": "arxiv",
    "version": 2
  }
}