Pith Number

pith:3UMPKLYI

pith:2026:3UMPKLYIXZLTKBEDXQZI4NDQLY

not attested not anchored not stored refs resolved

Induced subdivisions in graphs of large girth

Peiru Kuang, Yan Wang

Graphs with minimum degree at least k and girth above a fixed constant contain an induced subdivision of K_{k+1}.

arxiv:2605.17218 v1 · 2026-05-17 · math.CO

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\pithnumber{3UMPKLYIXZLTKBEDXQZI4NDQLY}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications 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

there exists an absolute constant g0 such that, for every integer k≥3, every graph G with δ(G)≥k and g(G)≥g0 contains an induced subdivision of K_{k+1}

C2weakest assumption

The proof depends on an induced variant of Mader's theorem (for every fixed s, η, D, every graph J with Δ(J)≤D, d(J)>s−2+η and sufficiently large girth contains an induced subdivision of K_s) whose own proof is not supplied in the abstract and is treated as a black-box ingredient.

C3one line summary

There exists an absolute constant g0 such that every graph with minimum degree at least k and girth at least g0 contains an induced subdivision of K_{k+1}.

References

36 extracted · 36 resolved · 0 Pith anchors

[1] N. Alon, S. Hoory and N. Linial, The Moore bound for irregular graphs,Graphs Combin.18(2002), no. 1, 53–57. 13 2002

[2] N. Alon and J. H. Spencer,The Probabilistic Method, Wiley, Hoboken, NJ, 4th ed., 2016 2016

[3] Bollob´ as and A 1998

[4] Buci´ c and R 2024

[5] Catlin, Haj´ os’ graph-coloring conjecture: variations and counterexamples,J 1979

Receipt and verification

First computed	2026-05-20T00:03:45.796918Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd18f52f08be57350483bc328e34705e2fa79cdc1eea343af950f485479e4a5f

Aliases

arxiv: 2605.17218 · arxiv_version: 2605.17218v1 · doi: 10.48550/arxiv.2605.17218 · pith_short_12: 3UMPKLYIXZLT · pith_short_16: 3UMPKLYIXZLTKBED · pith_short_8: 3UMPKLYI

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/3UMPKLYIXZLTKBEDXQZI4NDQLY \
  | 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: dd18f52f08be57350483bc328e34705e2fa79cdc1eea343af950f485479e4a5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0bd977e92df77531511b8137219735cbbfede865001be27a1b4169a4b4cd61ba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-17T01:32:55Z",
    "title_canon_sha256": "4ddc4dd9fcab9d21e2bca0fca9d5750345e079d6256c0dc8a8ddec02fdc42355"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17218",
    "kind": "arxiv",
    "version": 1
  }
}