Pith Number

pith:LAI7FJVD

pith:2026:LAI7FJVDMC3ACT5YD3PGXNBR46

not attested not anchored not stored refs resolved

The Outerplanar Tur\'{a}n Number of Double Stars

Changqing Xu, Chaofan Zhang, Yongxin Lan

The outerplanar Turán number for double stars S_{p,q} is determined exactly except for the case p=2 and q=3.

arxiv:2605.17330 v1 · 2026-05-17 · math.CO

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Record completeness

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4 Citations open

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Claims

C1strongest claim

We determine the exact values of ex_OP(n,S_{p,q}) for all q≥p≥2, with the sole exception of p=2 and q=3; for the latter, we establish a lower bound.

C2weakest assumption

The determination rests on the premise that the extremal outerplanar graphs for these forbidden subgraphs admit a uniform structural description (e.g., a cycle plus pendant trees of bounded size) that can be verified by case analysis on p and q; this structural claim is not stated in the abstract but is required for the exact formulas to hold.

C3one line summary

The paper computes exact outerplanar Turán numbers ex_OP(n, S_p,q) for q ≥ p ≥ 2 except p=2 q=3, where only a lower bound is shown.

References

20 extracted · 20 resolved · 1 Pith anchors

[1] Graph Theory 2008

[2] On some problems in graph theory, combinatorial analysis and combinatorial num- ber theory 1984

[3] Tur\'an densities of hypercubes 2012 · arXiv:1201.3587

[4] Subgraphs of a hypercube containing no small even cycles 1992

[5] Hexagon-free subgraphs of hypercubes 1993

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:52.449088Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5811f2a6a360b6014fb81ede6bb431e781e32b251c51823ba113e429be38b119

Aliases

arxiv: 2605.17330 · arxiv_version: 2605.17330v1 · doi: 10.48550/arxiv.2605.17330 · pith_short_12: LAI7FJVDMC3A · pith_short_16: LAI7FJVDMC3ACT5Y · pith_short_8: LAI7FJVD

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LAI7FJVDMC3ACT5YD3PGXNBR46 \
  | 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: 5811f2a6a360b6014fb81ede6bb431e781e32b251c51823ba113e429be38b119

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e46554f1ba2e1854cf3965b31635a5f0af562932cdc814fdf0fa25f93f66b2e4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-17T08:44:20Z",
    "title_canon_sha256": "8fda682d1cf35835b3d96cc13cffb4f4c34a0368f65e97692992941bf4c6753b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17330",
    "kind": "arxiv",
    "version": 1
  }
}