Pith Number

pith:VIQER2PF

pith:2026:VIQER2PFZ372N5BIHXIAVYH7YE

not attested not anchored not stored refs pending

An improved upper bound on the oriented diameter of graphs with diameter $4$

Jifu Lin, Lihua You, Xiaolin Wang

Every bridgeless graph with diameter 4 admits a strong orientation whose diameter is at most 18.

arxiv:2605.11667 v2 · 2026-05-12 · math.CO

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\usepackage{pith}
\pithnumber{VIQER2PFZ372N5BIHXIAVYH7YE}

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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

In this paper, we improve the upper bound of f(4) to 18.

C2weakest assumption

The proof relies on the existence of a specific orientation construction that achieves diameter 18 for arbitrary bridgeless diameter-4 graphs; if the case analysis or reduction steps in the full proof contain an uncovered configuration, the bound fails.

C3one line summary

The oriented diameter function satisfies f(4) ≤ 18, improving the prior upper bound of 21.

Receipt and verification

First computed	2026-06-09T02:08:43.774146Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa2048e9e5ceffa6f4283dd00ae0ffc11fb141663836c9f65ec678498ed8913c

Aliases

arxiv: 2605.11667 · arxiv_version: 2605.11667v2 · doi: 10.48550/arxiv.2605.11667 · pith_short_12: VIQER2PFZ372 · pith_short_16: VIQER2PFZ372N5BI · pith_short_8: VIQER2PF

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/VIQER2PFZ372N5BIHXIAVYH7YE \
  | 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: aa2048e9e5ceffa6f4283dd00ae0ffc11fb141663836c9f65ec678498ed8913c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c7bd1c166deb1a18779bee3777985c79f430c4a15a72f2ab2368c6fe166eba2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-12T07:27:23Z",
    "title_canon_sha256": "cc97e24d85d72df51e9ec347c65324b39cf4084c65816d320ab39d539f7de4f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.11667",
    "kind": "arxiv",
    "version": 2
  }
}