Pith Number

pith:FWQGGSAM

pith:2025:FWQGGSAMF5SKQ6UKU6KQNP4I3T

not attested not anchored not stored refs pending

Word-representability and comparability: Minimal forbidden induced subgraphs and cover number bounds

Benny George Kenkireth, Gopalan Sajith, Sreyas Sasidharan

Word-representable graphs on n vertices exist whose cover number by comparability graphs is Omega(log n).

arxiv:2502.06979 v4 · 2025-02-10 · cs.DM

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\usepackage{pith}
\pithnumber{FWQGGSAMF5SKQ6UKU6KQNP4I3T}

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Record completeness

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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

We demonstrate the existence of word-representable graphs on n vertices whose cover number by comparability graphs is Ω(log n), which establishes that the universal O(log n) upper bound is asymptotically tight for the class of word-representable graphs.

C2weakest assumption

The explicit constructions used to achieve the Ω(log n) lower bound on cover number produce graphs that are word-representable (i.e., admit semi-transitive orientations).

C3one line summary

Classifies minimal non-comparability graphs by word-representability and shows the cover number by comparability graphs is Θ(log n) for some word-representable graphs on n vertices.

Receipt and verification

First computed	2026-06-19T16:11:09.929307Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2da063480c2f64a87a8aa79506bf88dcf94b8bb2ddae583dd387050282ffac00

Aliases

arxiv: 2502.06979 · arxiv_version: 2502.06979v4 · doi: 10.48550/arxiv.2502.06979 · pith_short_12: FWQGGSAMF5SK · pith_short_16: FWQGGSAMF5SKQ6UK · pith_short_8: FWQGGSAM

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FWQGGSAMF5SKQ6UKU6KQNP4I3T \
  | 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: 2da063480c2f64a87a8aa79506bf88dcf94b8bb2ddae583dd387050282ffac00

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25236240ffdce6996b70b93ab2717ce178bd7060833581c1d6cb00a25cdffab9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2025-02-10T19:18:42Z",
    "title_canon_sha256": "08ee80f62c1bea86632f814bd879f667abb97b92ac7c760f4744dec0becc08e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.06979",
    "kind": "arxiv",
    "version": 4
  }
}