Pith Number

pith:OPRBCCD6

pith:2026:OPRBCCD6PN25UG6BEDL4UF4GUY

not attested not anchored not stored refs resolved

A non-hereditary Pollyanna class that is not strongly Pollyanna

Hongzhang Chen, Kaiyang Lan

A non-hereditary graph class exists that is Pollyanna but fails to be strongly Pollyanna for every k.

arxiv:2605.14547 v1 · 2026-05-14 · math.CO

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\usepackage{pith}
\pithnumber{OPRBCCD6PN25UG6BEDL4UF4GUY}

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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 construct a class C that is Pollyanna but, for every k ≥ 1, is not k-strongly Pollyanna; in particular C is not strongly Pollyanna.

C2weakest assumption

Graph classes are not required to be hereditary, allowing the construction of a non-hereditary class C that separates the Pollyanna and strongly Pollyanna properties.

C3one line summary

A non-hereditary graph class exists that is Pollyanna but not strongly Pollyanna.

References

7 extracted · 7 resolved · 0 Pith anchors

[1] M. Bria´ nski, J. Davies and B. Walczak, Separating polynomialχ-boundedness fromχ- boundedness,Combinatorica44(2024), 1–8 2024

[2] M. Chudnovsky, L. Cook, J. Davies and S. Oum, Reunitingχ-boundedness with polynomial χ-boundedness,J. Combin. Theory Ser. B176(2026), 30–73. 6 2026

[3] Esperet, Graph colorings, flows and perfect matchings, Habilitation Thesis, Universit´ e Grenoble Alpes, 2017 2017

[4] Gy´ arfas, On Ramsey covering-numbers, in:Infinite and Finite Sets (Colloq., Keszthely, 1973; Dedicated to P 1973

[5] Erd˝ os, Graph theory and probability,Canad 1959

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T23:39:05.751126Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73e211087e7b75da1bc120d7ca1786a610dae3ab7eb66269a375f98e21b6438d

Aliases

arxiv: 2605.14547 · arxiv_version: 2605.14547v1 · doi: 10.48550/arxiv.2605.14547 · pith_short_12: OPRBCCD6PN25 · pith_short_16: OPRBCCD6PN25UG6B · pith_short_8: OPRBCCD6

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/OPRBCCD6PN25UG6BEDL4UF4GUY \
  | 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: 73e211087e7b75da1bc120d7ca1786a610dae3ab7eb66269a375f98e21b6438d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4320d4d7aec82772077299adf131750d9fa0f1fe8a14b5e99eb20d2bd8952c03",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-14T08:26:12Z",
    "title_canon_sha256": "b95fc928dbfc9b66a204f1783cb8b9209853c2ec59f48a2a2538ea69108d68bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14547",
    "kind": "arxiv",
    "version": 1
  }
}