Pith Number

pith:5NODSS24

pith:2026:5NODSS244HUVF7WFPBAY2YRQUL

not attested not anchored not stored refs resolved

Min-1-Planarity is NP-Hard

Yuto Okada

Deciding whether a graph admits a min-1-planar drawing is NP-hard.

arxiv:2605.14834 v1 · 2026-05-14 · cs.CG · cs.DS

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\usepackage{pith}
\pithnumber{5NODSS244HUVF7WFPBAY2YRQUL}

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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 show that it is NP-hard to determine whether a given graph admits a min-1-planar drawing.

C2weakest assumption

The polynomial-time reduction from a known NP-complete problem to min-1-planarity testing is correct and preserves the yes/no answer.

C3one line summary

Deciding if a graph admits a min-1-planar drawing is NP-hard.

References

15 extracted · 15 resolved · 0 Pith anchors

[1] 2-level quasi-planarity or how caterpillars climb (spqr-)trees 2021

[2] More asymmetry yields faster matrix multiplication 2014 · doi:10.1137/1

[3] 5 Carla Binucci, Aaron Büngener, Giuseppe Di Battista, Walter Didimo, Vida Dujmović, Seok- Hee Hong, Michael Kaufmann, Giuseppe Liotta, Pat Morin, and Alessandra Tappini 2023 · doi:10.1007/s00453-016-0200-5

[4] 7 Carla Binucci, Emilio Di Giacomo, Walter Didimo, Fabrizio Montecchiani, Maurizio Patrignani, Antonios Symvonis, and Ioannis G · doi:10.7155/jgaa.v28i2.2925

[5] URL:https://doi.org/10.1016/j.tcs.2015.04.020, doi: 10.1016/J.TCS.2015.04.020. 8 Franz J. Brandenburg. Recognizing optimal 1-planar graphs in linear time.Algorith- mica, 80(1):1–28, 2015 · doi:10.1016/j.tcs.2015.04.020

Receipt and verification

First computed	2026-05-17T23:38:58.012733Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb5c394b5ce1e952fec578418d6230a2e931cd75277a74c58309d562d0de387b

Aliases

arxiv: 2605.14834 · arxiv_version: 2605.14834v1 · doi: 10.48550/arxiv.2605.14834 · pith_short_12: 5NODSS244HUV · pith_short_16: 5NODSS244HUVF7WF · pith_short_8: 5NODSS24

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/5NODSS244HUVF7WFPBAY2YRQUL \
  | 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: eb5c394b5ce1e952fec578418d6230a2e931cd75277a74c58309d562d0de387b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6580ff7eed5e60883a18a9772b13e0499501bba6f3776120865eb2f239ad1aeb",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2026-05-14T13:40:04Z",
    "title_canon_sha256": "449ec20e09f0985707c5d635de6070095b7fc83860812a88eb4b9dbb3d56eef3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14834",
    "kind": "arxiv",
    "version": 1
  }
}