Pith Number

pith:H2AAU2HC

pith:2026:H2AAU2HCXYH3JTP3NY4KIMLI6G

not attested not anchored not stored refs resolved

An excluded minor theorem for the 6-wheel

Weihua Yang, Yuqi Xu, Zijun Chen

This paper classifies every 3-connected nonplanar graph without a 6-wheel minor, completing the full characterization of W6-minor-free graphs.

arxiv:2605.15125 v1 · 2026-05-14 · math.CO

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\pithnumber{H2AAU2HCXYH3JTP3NY4KIMLI6G}

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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

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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

In this paper, we complete the characterization of W_6-minor-free graphs by determining the 3-connected nonplanar cases.

C2weakest assumption

Gubser's characterization of the planar 3-connected W_6-minor-free graphs is complete and correct, allowing the nonplanar cases to be exhaustively determined by the same minor-exclusion framework.

C3one line summary

All 3-connected nonplanar W_6-minor-free graphs are characterized.

References

14 extracted · 14 resolved · 0 Pith anchors

[1] G. Brinkmann and B. McKay. Fast generation of planar graphs.Match- Communications in Mathematical and in Computer Chemistry, 58(2):323–357, 2007. ISSN 0340-6253 2007

[2] G. Ding. A characterization of graphs with no octahedron minor.Journal of Graph Theory, 74(2):143–162, 2013 2013

[3] G. Ding and C. Liu. Excluding a small minor.Discrete Applied Mathematics, 161 (3):355–368, 2013 2013

[4] G.A. Dirac. A property of 4-chromatic graphs and some remarks on critical graphs. Journal of the London Mathematical Society, 1(1):85–92, 1952 1952

[5] A.B. Ferguson. Excluding two minors of the petersen graph.Louisiana State Uni- versity and Agricultural and Mechanical College, 2015 2015

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T21:40:25.668389Z
Last reissued	2026-05-17T21:57:18.994000Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

3e800a68e2be0fb4cdfb6e38a43168f1be208648cca56a1252394669f6123e68

Aliases

arxiv: 2605.15125 · arxiv_version: 2605.15125v1 · pith_short_12: H2AAU2HCXYH3 · pith_short_16: H2AAU2HCXYH3JTP3 · pith_short_8: H2AAU2HC

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/H2AAU2HCXYH3JTP3NY4KIMLI6G \
  | 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: 3e800a68e2be0fb4cdfb6e38a43168f1be208648cca56a1252394669f6123e68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50f42f72f85bafcc837605104292499a292e751a69afebab61b9127eea023d35",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-14T17:37:15Z",
    "title_canon_sha256": "9cda9a8812f9c0053c5ed60b72edd91cb257013ee28ac91a631d8a2c45ea47a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15125",
    "kind": "arxiv",
    "version": 1
  }
}