Pith Number

pith:YLH3ZWZL

pith:2026:YLH3ZWZLA4M3V7OJWHXPYN2SP5

not attested not anchored not stored refs resolved

Clique-width and induced topological minors

Amir Nikabadi, Jadwiga Czy\.zewska, Martin Milani\v{c}, Pawe{\l} Rafa{\l} Bieli\'nski, Pawe{\l} Rz\k{a}\.zewski

The class of graphs with no induced subdivision of H has bounded clique-width if and only if H is an induced subgraph of P4, the paw, or the diamond.

arxiv:2605.15453 v1 · 2026-05-14 · cs.DM · math.CO

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\usepackage{pith}
\pithnumber{YLH3ZWZLA4M3V7OJWHXPYN2SP5}

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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

✓ Portable graph bundle live · download bundle · merged state

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 that for a graph H, the class of graphs with no induced subdivision of H has bounded clique-width if and only if H is an induced subgraph of P4, the paw, or the diamond.

C2weakest assumption

The 'only if' direction relies on the existence of explicit constructions of graphs with unbounded clique-width that still avoid induced subdivisions of any H outside the three listed graphs; this construction step is invoked in the main theorem statement (abstract).

C3one line summary

The class of graphs with no induced subdivision of H has bounded clique-width if and only if H is an induced subgraph of P4, paw, or diamond.

References

18 extracted · 18 resolved · 0 Pith anchors

[1] Induced subgraphs and tree decom- positions I 2022

[2] Induced minor free graphs: Isomorphism and clique-width.Algorithmica, 80(1):29–47, 2018 2018

[3] Induced subgraphs and tree decompositions XIX 2025

[4] Induced subgraphs and tree decompositions XVI 2026

[5] Excluding induced subdivisions of the bull and related graphs.Journal of Graph Theory, 71(1):49–68, 2012 2012

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:59.399595Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2cfbcdb2b0719bafdc9b1eefc37527f4edf6a47a5b05aaebacda71884321846

Aliases

arxiv: 2605.15453 · arxiv_version: 2605.15453v1 · doi: 10.48550/arxiv.2605.15453 · pith_short_12: YLH3ZWZLA4M3 · pith_short_16: YLH3ZWZLA4M3V7OJ · pith_short_8: YLH3ZWZL

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/YLH3ZWZLA4M3V7OJWHXPYN2SP5 \
  | 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: c2cfbcdb2b0719bafdc9b1eefc37527f4edf6a47a5b05aaebacda71884321846

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e80d2280d7e82accf3852b1370b4bb198e29e6424dd5d05caee714722e171a3",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2026-05-14T22:35:09Z",
    "title_canon_sha256": "6cec1058e737ba18245adec54e28030453db6ed8ae0a75d5b6479a79d0a677b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15453",
    "kind": "arxiv",
    "version": 1
  }
}