Pith Number

pith:B2VHXCG5

pith:2025:B2VHXCG5EFRSQL6TM4BFG2X2IL

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Unavoidable substructures in large and infinite $2$-edge-connected graphs

M. N. Ellingham, Sarah Allred

Every large or infinite 2-edge-connected graph contains one of a specific list of induced subgraphs that includes chains of pinched super-clean ladders.

arxiv:2503.21574 v4 · 2025-03-27 · math.CO

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\pithnumber{B2VHXCG5EFRSQL6TM4BFG2X2IL}

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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

We prove the existence of ubiquitous structures in 2-edge-connected graphs known as chains of pinched super-clean ladders, and incorporate these into a presentation of the unavoidable large induced subgraphs for large and infinite 2-edge-connected graphs.

C2weakest assumption

The prior unavoidable-set result for 2-connected graphs (Allred, Ding, Oporowski) can be adapted to the strictly weaker 2-edge-connected setting by inserting the new ladder-chain structures without requiring additional connectivity assumptions or case distinctions that would invalidate the list.

C3one line summary

The unavoidable large induced subgraphs of 2-edge-connected graphs are characterized via chains of pinched super-clean ladders, extending prior results for connected and 2-connected graphs.

Receipt and verification

First computed	2026-06-09T02:08:29.514625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0eaa7b88dd2163282fd36702536afa42e3245ebd43ad4d8bb6dacce7b43bb980

Aliases

arxiv: 2503.21574 · arxiv_version: 2503.21574v4 · doi: 10.48550/arxiv.2503.21574 · pith_short_12: B2VHXCG5EFRS · pith_short_16: B2VHXCG5EFRSQL6T · pith_short_8: B2VHXCG5

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/B2VHXCG5EFRSQL6TM4BFG2X2IL \
  | 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: 0eaa7b88dd2163282fd36702536afa42e3245ebd43ad4d8bb6dacce7b43bb980

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "634980765598aefc8981ff02e37d93f4c20254d3da82d7e2227d84819b72a68c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-03-27T14:53:06Z",
    "title_canon_sha256": "2abc4e2103557f65ac9b0097bc797af8b4ad48d0024e9393dcf1dd09fece9fd1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2503.21574",
    "kind": "arxiv",
    "version": 4
  }
}